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<!--XBRL Document Created with Wdesk from Workiva-->
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    <link:label id="lab_us-gaap_CurrentStateAndLocalTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentStateAndLocalTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Current State and Local Tax Expense (Benefit)</link:label>
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    <link:label id="lab_us-gaap_LeaseholdImprovementsMember_1e7d2bc7-1737-4b6c-8364-0ab56cb223b8_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Improvements</link:label>
    <link:label id="lab_us-gaap_LeaseholdImprovementsMember_label_en-US" xlink:label="lab_us-gaap_LeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Leasehold Improvements [Member]</link:label>
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    <link:label id="lab_dgii_TotalAssetsbySegmentAbstract_09e09d64-1058-4a45-9516-34d3b3e5a077_terseLabel_en-US" xlink:label="lab_dgii_TotalAssetsbySegmentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total Assets by Segment [Abstract]</link:label>
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    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_87848f70-d6ce-44c0-9427-2498aea5487e_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred stock, shares outstanding</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts_37ac226b-4ab5-45f7-9211-1021ab5d4f40_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Acquisition costs</link:label>
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    <link:label id="lab_dei_SecurityExchangeName_6d3bc64e-cde2-44ea-ad0b-86fe75519664_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Security Exchange Name</link:label>
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    <link:label id="lab_us-gaap_EMEAMember_99232780-32c4-4de4-9889-30815b6ff9ca_terseLabel_en-US" xlink:label="lab_us-gaap_EMEAMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Europe, Middle East &amp; Africa</link:label>
    <link:label id="lab_us-gaap_EMEAMember_label_en-US" xlink:label="lab_us-gaap_EMEAMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">EMEA [Member]</link:label>
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    <link:label id="lab_dgii_InfrastructureMgmtMember_60353894-a373-4479-9735-fddbc0ffbe57_terseLabel_en-US" xlink:label="lab_dgii_InfrastructureMgmtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Infrastructure Mgmt.</link:label>
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    <link:label id="lab_us-gaap_PaymentForContingentConsiderationLiabilityFinancingActivities_1399dff6-2cb1-4e1a-bd97-ce07f48183dc_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentForContingentConsiderationLiabilityFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments for contingent consideration</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAdditionalDisclosuresAbstract_75f8514c-3aff-41b9-ab9a-08406bfa73f9_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAdditionalDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Options, Additional Disclosures [Abstract]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAdditionalDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAdditionalDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Options, Additional Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAdditionalDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAdditionalDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAdditionalDisclosuresAbstract" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAdditionalDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber_78e8a209-cba2-444e-a7b3-901481036c17_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Options Outstanding, Exercisable</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Options, Exercisable, Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_dgii_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfHoursPerWeekEmployed_cfea370a-e1b9-493e-a9b5-6e613d725156_terseLabel_en-US" xlink:label="lab_dgii_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfHoursPerWeekEmployed" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of hours per week employed</link:label>
    <link:label id="lab_dgii_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfHoursPerWeekEmployed_label_en-US" xlink:label="lab_dgii_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfHoursPerWeekEmployed" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Number of Hours Per Week Employed</link:label>
    <link:label id="lab_dgii_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfHoursPerWeekEmployed_documentation_en-US" xlink:label="lab_dgii_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfHoursPerWeekEmployed" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Number of Hours Per Week Employed</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dgii_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfHoursPerWeekEmployed" xlink:href="dgii-20220930.xsd#dgii_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfHoursPerWeekEmployed"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dgii_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfHoursPerWeekEmployed" xlink:to="lab_dgii_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfHoursPerWeekEmployed" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DecreaseInUnrecognizedTaxBenefitsIsReasonablyPossible_83594dda-a7cb-4f52-beb5-a11b1716f298_netLabel_en-US" xlink:label="lab_us-gaap_DecreaseInUnrecognizedTaxBenefitsIsReasonablyPossible" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Decrease in unrecognized tax benefits that is reasonably possible</link:label>
    <link:label id="lab_us-gaap_DecreaseInUnrecognizedTaxBenefitsIsReasonablyPossible_label_en-US" xlink:label="lab_us-gaap_DecreaseInUnrecognizedTaxBenefitsIsReasonablyPossible" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Decrease in Unrecognized Tax Benefits is Reasonably Possible</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DecreaseInUnrecognizedTaxBenefitsIsReasonablyPossible" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DecreaseInUnrecognizedTaxBenefitsIsReasonablyPossible"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DecreaseInUnrecognizedTaxBenefitsIsReasonablyPossible" xlink:to="lab_us-gaap_DecreaseInUnrecognizedTaxBenefitsIsReasonablyPossible" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockValue_3bbcd586-1d0c-407c-960b-9db41dce42c3_verboseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred stock, $.01 par value; 2,000,000 shares authorized; none issued and outstanding</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PreferredStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockValue" xlink:to="lab_us-gaap_PreferredStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharesIssuedPricePerShare_809da278-ce05-48cb-8c3d-aa64004b6849_terseLabel_en-US" xlink:label="lab_us-gaap_SharesIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Shares Issued, Price Per Share</link:label>
    <link:label id="lab_us-gaap_SharesIssuedPricePerShare_label_en-US" xlink:label="lab_us-gaap_SharesIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Shares Issued, Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharesIssuedPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_SharesIssuedPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharesIssuedPricePerShare" xlink:to="lab_us-gaap_SharesIssuedPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsMember_c9b03211-f4f8-4829-ab86-d724ad7e3709_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Retained Earnings</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Retained Earnings [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_RetainedEarningsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsMember" xlink:to="lab_us-gaap_RetainedEarningsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dgii_ExercisePriceRangeSevenMember_77918479-05c1-496d-88f2-765a75177419_terseLabel_en-US" xlink:label="lab_dgii_ExercisePriceRangeSevenMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">$17.95 - $18.20</link:label>
    <link:label id="lab_dgii_ExercisePriceRangeSevenMember_label_en-US" xlink:label="lab_dgii_ExercisePriceRangeSevenMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Exercise Price Range Seven [Member]</link:label>
    <link:label id="lab_dgii_ExercisePriceRangeSevenMember_documentation_en-US" xlink:label="lab_dgii_ExercisePriceRangeSevenMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Exercise Price Range Seven [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dgii_ExercisePriceRangeSevenMember" xlink:href="dgii-20220930.xsd#dgii_ExercisePriceRangeSevenMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dgii_ExercisePriceRangeSevenMember" xlink:to="lab_dgii_ExercisePriceRangeSevenMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesLeasingArrangements_b4d40542-dff3-49a6-a33c-113b6e1e1572_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesLeasingArrangements" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Lease asset</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesLeasingArrangements_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesLeasingArrangements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Deferred Tax Liabilities, Leasing Arrangements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxLiabilitiesLeasingArrangements" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DeferredTaxLiabilitiesLeasingArrangements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxLiabilitiesLeasingArrangements" xlink:to="lab_us-gaap_DeferredTaxLiabilitiesLeasingArrangements" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StandardProductWarrantyAccrualPayments_3aa4db95-4035-4b62-b921-e07c7eeabf16_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_StandardProductWarrantyAccrualPayments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Settlements made</link:label>
    <link:label id="lab_us-gaap_StandardProductWarrantyAccrualPayments_label_en-US" xlink:label="lab_us-gaap_StandardProductWarrantyAccrualPayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Standard Product Warranty Accrual, Decrease for Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StandardProductWarrantyAccrualPayments" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_StandardProductWarrantyAccrualPayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StandardProductWarrantyAccrualPayments" xlink:to="lab_us-gaap_StandardProductWarrantyAccrualPayments" xlink:type="arc" order="1"/>
    <link:label id="lab_dgii_ExercisePriceRangeThreeMember_3fa55076-b948-4a82-b73f-6b124cca1e6b_terseLabel_en-US" xlink:label="lab_dgii_ExercisePriceRangeThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">$10.35 - $11.23</link:label>
    <link:label id="lab_dgii_ExercisePriceRangeThreeMember_label_en-US" xlink:label="lab_dgii_ExercisePriceRangeThreeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Exercise Price Range Three [Member]</link:label>
    <link:label id="lab_dgii_ExercisePriceRangeThreeMember_documentation_en-US" xlink:label="lab_dgii_ExercisePriceRangeThreeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Exercise Price Range Three [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dgii_ExercisePriceRangeThreeMember" xlink:href="dgii-20220930.xsd#dgii_ExercisePriceRangeThreeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dgii_ExercisePriceRangeThreeMember" xlink:to="lab_dgii_ExercisePriceRangeThreeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_9afda143-3266-4236-a18f-1f7fea9780ac_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounts receivable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (Decrease) in Accounts Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_IncreaseDecreaseInAccountsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid_31f960fe-11dd-4333-a655-df0ce2e7ad76_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accrual for property, equipment, improvements and certain other intangibles assets</link:label>
    <link:label id="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid_label_en-US" xlink:label="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Capital Expenditures Incurred but Not yet Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_CapitalExpendituresIncurredButNotYetPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:to="lab_us-gaap_CapitalExpendituresIncurredButNotYetPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_dgii_RestructuringReversalChargeNet_b2efdbef-aa96-4b07-b8eb-bd16566819ae_terseLabel_en-US" xlink:label="lab_dgii_RestructuringReversalChargeNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restructuring Charges</link:label>
    <link:label id="lab_dgii_RestructuringReversalChargeNet_label_en-US" xlink:label="lab_dgii_RestructuringReversalChargeNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restructuring (Reversal) Charge, Net</link:label>
    <link:label id="lab_dgii_RestructuringReversalChargeNet_documentation_en-US" xlink:label="lab_dgii_RestructuringReversalChargeNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restructuring (Reversal) Charge, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dgii_RestructuringReversalChargeNet" xlink:href="dgii-20220930.xsd#dgii_RestructuringReversalChargeNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dgii_RestructuringReversalChargeNet" xlink:to="lab_dgii_RestructuringReversalChargeNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_f4aa481c-96f6-4b85-adc7-4753ce5cdd3b_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property, Plant and Equipment [Line Items]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property, Plant and Equipment [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PropertyPlantAndEquipmentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityWellKnownSeasonedIssuer_3a313930-bbeb-46d1-8b04-4061ddfc3481_terseLabel_en-US" xlink:label="lab_dei_EntityWellKnownSeasonedIssuer" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Well-known Seasoned Issuer</link:label>
    <link:label id="lab_dei_EntityWellKnownSeasonedIssuer_label_en-US" xlink:label="lab_dei_EntityWellKnownSeasonedIssuer" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Well-known Seasoned Issuer</link:label>
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    <link:label id="lab_dei_EntityVoluntaryFilers_abc510d4-5c82-458c-a1a4-1a8879d15ab8_terseLabel_en-US" xlink:label="lab_dei_EntityVoluntaryFilers" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Voluntary Filers</link:label>
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    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedInPeriodFairValue1_7291e955-7a0e-4218-9068-0802c42be583_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedInPeriodFairValue1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total grant date fair value of shares vested</link:label>
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    <link:label id="lab_us-gaap_LongTermDebt_e57a0661-a978-447b-b3ee-8e5613760468_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-term Debt</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_b7fbe314-8f9e-4c5d-8916-843ca7e28150_verboseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Investing activities:</link:label>
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    <link:label id="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTextBlock_bfb9b73e-5b72-4a23-9dd8-5c2a96df5823_terseLabel_en-US" xlink:label="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Total Assets by Segment</link:label>
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    <link:label id="lab_us-gaap_BalanceSheetLocationDomain_faf0e2ee-9e17-4e43-bdbf-cf8be7e3b8b1_terseLabel_en-US" xlink:label="lab_us-gaap_BalanceSheetLocationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Balance Sheet Location [Domain]</link:label>
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    <link:label id="lab_us-gaap_UnrecognizedTaxBenefits_ace1a8f7-cdb6-4968-81e4-3d3dbb2381c6_periodStartLabel_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefits" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unrecognized tax benefits, beginning balance</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxAuthorityDomain_8ef14993-1a33-4d61-a6c1-80539b101655_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Tax Authority [Domain]</link:label>
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    <link:label id="lab_dei_EntityAddressStateOrProvince_ea79a0cf-3a8b-4f1f-94a0-655433b1f6d9_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, State or Province</link:label>
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    <link:label id="lab_us-gaap_GoodwillLineItems_1bf14c47-4062-41ce-88ae-603306d72a0a_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Goodwill [Line Items]</link:label>
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    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss_e388ecce-ee1e-4e82-bad4-ad2df0e3fda4_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net income</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxContingencyLineItems_dc06bdf2-93db-42c2-b696-5613eb23de7d_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxContingencyLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Tax Contingency [Line Items]</link:label>
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    <link:label id="lab_us-gaap_InventoryWorkInProcessNetOfReserves_3a0b0447-df59-46a9-bc51-b9662eb5fa5a_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryWorkInProcessNetOfReserves" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Work in process</link:label>
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    <link:label id="lab_us-gaap_PaymentsToAcquireProductiveAssets_9c46b08e-1650-4fdd-817a-e68277146a3b_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireProductiveAssets" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Purchase of property, equipment, improvements and certain other intangible assets</link:label>
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    <link:label id="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrent_fdd0f2c9-446b-41b8-8bf2-be6d2f40c9b9_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidExpenseAndOtherAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other current assets</link:label>
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    <link:label id="lab_dgii_IoTSolutionsMember_4cf3a5ca-ae97-496d-8a92-3d56da69fedd_terseLabel_en-US" xlink:label="lab_dgii_IoTSolutionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">IoT Solutions</link:label>
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    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_8e1dfa29-09e4-4581-8922-0f552c50620b_verboseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue</link:label>
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    <link:label id="lab_us-gaap_EmployeeStockOptionMember_8f982534-57ab-49e8-9564-8e33898e9109_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stock Options</link:label>
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    <link:label id="lab_us-gaap_OtherPensionPlansDefinedBenefitMember_f5ba5b22-d535-4d63-950c-da993bcabf36_terseLabel_en-US" xlink:label="lab_us-gaap_OtherPensionPlansDefinedBenefitMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Defined contribution plan</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationsAbstract_6f2dda2c-207e-45c3-8e1c-49e4b627df30_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Combinations [Abstract]</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationsAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Combinations [Abstract]</link:label>
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    <link:label id="lab_srt_MaximumMember_209c8466-bf1d-4461-b72c-8153b5fd0ae9_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Maximum [Member]</link:label>
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    <link:label id="lab_dgii_EarnOutPaymentsMember_df05c704-0149-4e38-a0f7-756b7e4581af_terseLabel_en-US" xlink:label="lab_dgii_EarnOutPaymentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Earn-out payments</link:label>
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    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_7c72085b-a4a6-413c-93eb-5374ed6745ab_terseLabel_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Payment Arrangement [Abstract]</link:label>
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    <link:label id="lab_us-gaap_InventoryRawMaterialsNetOfReserves_475e88dd-09ac-4bd2-a391-125167861139_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryRawMaterialsNetOfReserves" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Raw materials</link:label>
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    <link:label id="lab_us-gaap_AwardTypeAxis_30dbe93c-9daa-454b-9ecb-78c3b982da7d_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Award Type [Axis]</link:label>
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    <link:label id="lab_dgii_BaseRateElectionDomain_48516074-df7b-4b37-880d-edba89a4045c_terseLabel_en-US" xlink:label="lab_dgii_BaseRateElectionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Base Rate Election [Domain]</link:label>
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    <link:label id="lab_dgii_BaseRateElectionDomain_documentation_en-US" xlink:label="lab_dgii_BaseRateElectionDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Base Rate Election [Domain]</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_b62935e0-1fa8-4ebc-b996-89e15b54db01_verboseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Financing activities:</link:label>
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    <link:label id="lab_us-gaap_StockholdersEquity_84d1061f-2d0d-43b5-bcb4-29db5d6c0fdd_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total stockholders&#8217; equity</link:label>
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    <link:label id="lab_dei_CityAreaCode_908ae011-da61-423a-9983-e6f635a26e6d_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">City Area Code</link:label>
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    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_57e65fe9-df18-4778-a3d0-16c43039abb5_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Taxes paid for net share settlement of share-based payment awards</link:label>
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    <link:label id="lab_dgii_ConsoleServersMember_7d49b566-aaa7-4be3-83d9-4233711fb641_terseLabel_en-US" xlink:label="lab_dgii_ConsoleServersMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Console Servers</link:label>
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    <link:label id="lab_dgii_ConsoleServersMember_documentation_en-US" xlink:label="lab_dgii_ConsoleServersMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Console Servers</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife_c7c1fa86-8704-41be-8b85-1017cae60e7d_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property, equipment and improvements depreciation life</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property, Plant and Equipment, Useful Life</link:label>
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    <link:label id="lab_us-gaap_StockholdersEquityAbstract_b4387d2e-c0f8-442d-a624-18af589ffafd_verboseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stockholders&#8217; equity:</link:label>
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    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrent_183c9c31-8390-4694-b236-695100a8b223_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating lease liabilities</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrent_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating Lease, Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_OperatingLeaseLiabilityNoncurrent"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRateMaximum_cfcbfc34-d94b-4cb6-b27a-fb71874a346f_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRateMaximum" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Expected volatility rate, maximum</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRateMaximum" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRateMaximum"/>
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    <link:label id="lab_dgii_ChangeInContractWithCustomerLiabilityRollForward_2c029670-53d7-4608-a55d-48ee466b646d_terseLabel_en-US" xlink:label="lab_dgii_ChangeInContractWithCustomerLiabilityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unearned Revenue [Roll Forward]</link:label>
    <link:label id="lab_dgii_ChangeInContractWithCustomerLiabilityRollForward_label_en-US" xlink:label="lab_dgii_ChangeInContractWithCustomerLiabilityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Change In Contract With Customer, Liability [Roll Forward]</link:label>
    <link:label id="lab_dgii_ChangeInContractWithCustomerLiabilityRollForward_documentation_en-US" xlink:label="lab_dgii_ChangeInContractWithCustomerLiabilityRollForward" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Change In Contract With Customer, Liability [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dgii_ChangeInContractWithCustomerLiabilityRollForward" xlink:href="dgii-20220930.xsd#dgii_ChangeInContractWithCustomerLiabilityRollForward"/>
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    <link:label id="lab_dgii_ExercisePriceRangeTwoMember_da16579f-57cf-430e-8deb-f92da3c96fd9_terseLabel_en-US" xlink:label="lab_dgii_ExercisePriceRangeTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">$9.04 - $10.33</link:label>
    <link:label id="lab_dgii_ExercisePriceRangeTwoMember_label_en-US" xlink:label="lab_dgii_ExercisePriceRangeTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Exercise Price Range Two [Member]</link:label>
    <link:label id="lab_dgii_ExercisePriceRangeTwoMember_documentation_en-US" xlink:label="lab_dgii_ExercisePriceRangeTwoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Exercise Price Range Two [Member]</link:label>
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    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense_59edbb53-9152-4a5e-896b-19df8680aabb_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income tax benefit</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Payment Arrangement, Expense, Tax Benefit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationTaxBenefitFromCompensationExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharePrice_8edcadb7-a647-4fe8-bb07-6e780ce19d06_terseLabel_en-US" xlink:label="lab_us-gaap_SharePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Closing Stock Price</link:label>
    <link:label id="lab_us-gaap_SharePrice_label_en-US" xlink:label="lab_us-gaap_SharePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_SharePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharePrice" xlink:to="lab_us-gaap_SharePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_5d80117b-4683-4cda-8b61-a69c5cb25a22_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restricted Stock Units</link:label>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_label_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restricted Stock Units (RSUs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockUnitsRSUMember" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_RestrictedStockUnitsRSUMember"/>
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    <link:label id="lab_us-gaap_ValuationAllowancesAndReservesChargedToOtherAccounts_afb8fa62-9abe-4110-9f71-dc7943c0ca57_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationAllowancesAndReservesChargedToOtherAccounts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Charged to Other Accounts</link:label>
    <link:label id="lab_us-gaap_ValuationAllowancesAndReservesChargedToOtherAccounts_label_en-US" xlink:label="lab_us-gaap_ValuationAllowancesAndReservesChargedToOtherAccounts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">SEC Schedule, 12-09, Valuation Allowances and Reserves, Additions, Charge to Other Account</link:label>
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    <link:label id="lab_dgii_A2021Member_8a1f4c3d-430a-45f2-a63f-c3b6f56cce9c_terseLabel_en-US" xlink:label="lab_dgii_A2021Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2021</link:label>
    <link:label id="lab_dgii_A2021Member_label_en-US" xlink:label="lab_dgii_A2021Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2021 [Member]</link:label>
    <link:label id="lab_dgii_A2021Member_documentation_en-US" xlink:label="lab_dgii_A2021Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2021</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dgii_A2021Member" xlink:href="dgii-20220930.xsd#dgii_A2021Member"/>
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    <link:label id="lab_us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch_ec1313fb-ce2e-4058-83fd-e8ad129dcf83_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Employers percent of matching contributions</link:label>
    <link:label id="lab_us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch_label_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanEmployerMatchingContributionPercentOfMatch" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Defined Contribution Plan, Employer Matching Contribution, Percent of Match</link:label>
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    <link:label id="lab_us-gaap_BusinessAcquisitionLineItems_86f74cf8-9fe2-4e07-8495-95ac9f725598_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Acquisition [Line Items]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionLineItems_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Acquisition [Line Items]</link:label>
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    <link:label id="lab_dei_EntityRegistrantName_d001b73d-d823-4ce8-93bb-a3adbcf6d018_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Registrant Name</link:label>
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    <link:label id="lab_us-gaap_SharebasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeOutstandingOptionsWeightedAverageExercisePriceBeginningBalance1_1df9bf9e-d0f7-44e8-acbc-dd6213852108_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeOutstandingOptionsWeightedAverageExercisePriceBeginningBalance1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Weighted Average Exercise Price, Options Outstanding</link:label>
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    <link:label id="lab_dgii_The2021PlanMember_25378621-1f29-4c34-9c0f-31e619cdc010_terseLabel_en-US" xlink:label="lab_dgii_The2021PlanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The 2021 Plan</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationOtherAdjustments_79832258-d147-4faa-b68c-351322163405_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationOtherAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other, net</link:label>
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    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_6197c79c-62e3-4033-8d84-96a9d8fb7e31_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounts receivable, net</link:label>
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    <link:label id="lab_dgii_StandardProductWarrantyAccrualTermMinimum_f01abca0-750f-4bb4-ae17-48da0b9c83d5_terseLabel_en-US" xlink:label="lab_dgii_StandardProductWarrantyAccrualTermMinimum" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Warranty period products, minimum</link:label>
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    <link:label id="lab_dei_EntityTaxIdentificationNumber_92ee3fcd-4363-418d-8c39-156e8b7d5750_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Tax Identification Number</link:label>
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    <link:label id="lab_dei_DocumentFiscalPeriodFocus_cf5435ed-d3c4-447b-b2aa-888eee3bd67a_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Fiscal Period Focus</link:label>
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    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_7d843b4c-c904-4ccb-84fb-a1d694817524_terseLabel_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revolving Credit Facility</link:label>
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    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_label_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revolving Credit Facility [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevolvingCreditFacilityMember" xlink:to="lab_us-gaap_RevolvingCreditFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_302143f6-89f7-4b51-b083-d3eb722731c9_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementFrequencyAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Measurement Frequency [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementFrequencyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_FairValueByMeasurementFrequencyAxis"/>
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    <link:label id="lab_us-gaap_ValuationAllowanceOfDeferredTaxAssetsMember_7ab13ada-beb5-4049-bd5a-a63d2e503af5_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationAllowanceOfDeferredTaxAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Valuation allowance - deferred tax assets</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeTable_39e94727-66f1-456e-a784-86b5043b55f0_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Payment Arrangement, Option, Exercise Price Range [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Payment Arrangement, Option, Exercise Price Range [Table]</link:label>
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    <link:label id="lab_us-gaap_LeaseCostTableTextBlock_5a3e30bf-779c-4ef6-8bee-e228c83f2225_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseCostTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Components of Lease Cost</link:label>
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    <link:label id="lab_dgii_SalesRevenueGoodsNetExportedMember_c804ccbe-cac8-427a-9df2-8310664d65cc_terseLabel_en-US" xlink:label="lab_dgii_SalesRevenueGoodsNetExportedMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">U.S. Export Net Sales</link:label>
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    <link:label id="lab_dgii_SalesRevenueGoodsNetExportedMember_documentation_en-US" xlink:label="lab_dgii_SalesRevenueGoodsNetExportedMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sales Revenue, Goods, Net, Exported [Member]</link:label>
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    <link:label id="lab_srt_StatementGeographicalAxis_bc1b4270-3454-4080-97ea-f7839f61da66_terseLabel_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:label id="lab_srt_StatementGeographicalAxis_label_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementGeographicalAxis" xlink:href="https://xbrl.fasb.org/srt/2021/elts/srt-2021-01-31.xsd#srt_StatementGeographicalAxis"/>
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    <link:label id="lab_us-gaap_ProductMember_85dfc55d-e86b-4e46-b99b-09dc91636360_terseLabel_en-US" xlink:label="lab_us-gaap_ProductMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Product</link:label>
    <link:label id="lab_us-gaap_ProductMember_label_en-US" xlink:label="lab_us-gaap_ProductMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Product [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProductMember" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ProductMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProductMember" xlink:to="lab_us-gaap_ProductMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dgii_TimingOfContingentConsiderationAxis_0457d2ff-8db0-45ef-b25b-e6d6e2d51baa_terseLabel_en-US" xlink:label="lab_dgii_TimingOfContingentConsiderationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Timing of Contingent Consideration [Axis]</link:label>
    <link:label id="lab_dgii_TimingOfContingentConsiderationAxis_label_en-US" xlink:label="lab_dgii_TimingOfContingentConsiderationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Timing of Contingent Consideration [Axis]</link:label>
    <link:label id="lab_dgii_TimingOfContingentConsiderationAxis_documentation_en-US" xlink:label="lab_dgii_TimingOfContingentConsiderationAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Timing of Contingent Consideration</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential_2a9d10f6-ea46-45d4-a705-21a6d8e1e416_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxReconciliationForeignIncomeTaxRateDifferential" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Foreign operations</link:label>
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    <link:label id="lab_dgii_ContingentConsiderationMember_d939aaf9-7900-43d2-bdb5-b68dd738f0af_terseLabel_en-US" xlink:label="lab_dgii_ContingentConsiderationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contingent Consideration</link:label>
    <link:label id="lab_dgii_ContingentConsiderationMember_05724dc4-5544-4c1d-adb7-b5fc03498345_verboseLabel_en-US" xlink:label="lab_dgii_ContingentConsiderationMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contingent consideration on acquired business</link:label>
    <link:label id="lab_dgii_ContingentConsiderationMember_label_en-US" xlink:label="lab_dgii_ContingentConsiderationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contingent Consideration [Member]</link:label>
    <link:label id="lab_dgii_ContingentConsiderationMember_documentation_en-US" xlink:label="lab_dgii_ContingentConsiderationMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contingent Consideration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dgii_ContingentConsiderationMember" xlink:href="dgii-20220930.xsd#dgii_ContingentConsiderationMember"/>
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    <link:label id="lab_us-gaap_CorporateMember_db399d08-e154-450a-9a74-914089a85c03_terseLabel_en-US" xlink:label="lab_us-gaap_CorporateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unallocated</link:label>
    <link:label id="lab_us-gaap_CorporateMember_label_en-US" xlink:label="lab_us-gaap_CorporateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Corporate Segment [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CorporateMember" xlink:to="lab_us-gaap_CorporateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_a0554db7-99ab-4996-97ab-47d0f7b61f7d_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net cash provided by financing activities</link:label>
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    <link:label id="lab_us-gaap_TreasuryStockValue_e2c70627-2fca-432c-bde1-1f329e261b48_negatedLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockValue" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Treasury stock, at cost, 6,412,812 and 6,390,645 shares</link:label>
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    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
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    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock_a9cd6faa-5fa1-4642-8f86-c4a1dd02bfde_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue Recognition</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue from Contract with Customer [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_RevenueFromContractWithCustomerPolicyTextBlock"/>
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    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_0a0b7b52-583b-487b-a305-656a76eda63d_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Diluted (shares)</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic_04701131-693c-42bd-b71d-d90c03dae1a2_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">United States</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Domestic</link:label>
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    <link:label id="lab_us-gaap_DebtConversionOriginalDebtAmount1_96ff10e8-624d-439b-b714-83d8782cbe81_terseLabel_en-US" xlink:label="lab_us-gaap_DebtConversionOriginalDebtAmount1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Term debt refinanced as credit facility</link:label>
    <link:label id="lab_us-gaap_DebtConversionOriginalDebtAmount1_label_en-US" xlink:label="lab_us-gaap_DebtConversionOriginalDebtAmount1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Conversion, Original Debt, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtConversionOriginalDebtAmount1" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DebtConversionOriginalDebtAmount1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtConversionOriginalDebtAmount1" xlink:to="lab_us-gaap_DebtConversionOriginalDebtAmount1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_c1e43e70-f868-4978-9425-4eda2127e3c3_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Tax Disclosure [Text Block]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Tax Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_IncomeTaxDisclosureTextBlock"/>
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    <link:label id="lab_us-gaap_TransferredAtPointInTimeMember_5b5b29dc-ca1e-454a-ad6a-079244899ab3_terseLabel_en-US" xlink:label="lab_us-gaap_TransferredAtPointInTimeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Transferred at a point in time</link:label>
    <link:label id="lab_us-gaap_TransferredAtPointInTimeMember_label_en-US" xlink:label="lab_us-gaap_TransferredAtPointInTimeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Transferred at Point in Time [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransferredAtPointInTimeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_TransferredAtPointInTimeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TransferredAtPointInTimeMember" xlink:to="lab_us-gaap_TransferredAtPointInTimeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_17ad002d-b4ef-4c97-adfe-70f1b91d8e04_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt instrument, basis spread on variable rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Instrument, Basis Spread on Variable Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:to="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_ad5062a0-3429-46ed-9dbc-d0a2df2e845a_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityAxis_16ce5622-346a-40f9-b9b2-a0603c0a7b70_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityAxis_label_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_CreditFacilityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityAxis" xlink:to="lab_us-gaap_CreditFacilityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_8a91208a-8698-45b8-9d45-3d4b152fd205_verboseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_b0294d29-76cd-4147-a521-7184f5c13d00_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_bba7a4e1-7729-4f29-931b-a21ace9c27ba_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, Address Line One</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine2_c7c9be29-13c8-4c22-a96d-4bdf0afc78cc_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, Address Line Two</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine2" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_EntityAddressAddressLine2"/>
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    <link:label id="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_9e68f424-bc10-4727-af70-6696558192de_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Less accumulated depreciation and amortization</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:to="lab_us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueEmployeeStockPurchasePlan_19835554-8163-4d8f-99d6-e0a7b13f64a8_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueEmployeeStockPurchasePlan" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Employee stock purchase issuances</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_68a29fd9-158e-4946-82ec-63c84470f21b_verboseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating activities:</link:label>
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    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpenseMember_3febb0e3-31a9-4c35-a342-55f60c166d3d_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpenseMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">General and Administrative</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpenseMember_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpenseMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">General and Administrative Expense [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpenseMember" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpenseMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_4c0d4d6c-e0bb-4196-98c0-23b5d028ce5d_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Principles of Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_23894e02-1d54-40b9-a099-931b91f1dcca_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Shell Company</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_bc194485-9dda-4208-b3b4-faafaa10f4ac_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Expected term</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Expected Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1"/>
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    <link:label id="lab_us-gaap_LiabilitiesCurrent_03ef61b0-f001-49af-a700-df33785966f3_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total current liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liabilities, Current</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrent" xlink:to="lab_us-gaap_LiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockMember_023a3679-19c0-447c-9d33-118cc7ec9aeb_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Employee Stock</link:label>
    <link:label id="lab_us-gaap_EmployeeStockMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Employee Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_EmployeeStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockMember" xlink:to="lab_us-gaap_EmployeeStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingenciesTable_97e135fe-8f96-4481-a717-6190036a6fe2_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingenciesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Loss Contingencies [Table]</link:label>
    <link:label id="lab_us-gaap_LossContingenciesTable_label_en-US" xlink:label="lab_us-gaap_LossContingenciesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Loss Contingencies [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingenciesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_LossContingenciesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingenciesTable" xlink:to="lab_us-gaap_LossContingenciesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent_ecf222d7-5d2b-4277-852e-3d657c45261f_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Percent of employees' gross pay for employer match</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DefinedContributionPlanEmployerMatchingContributionPercent"/>
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    <link:label id="lab_dei_CurrentFiscalYearEndDate_0768eccb-e1a5-48d7-bdaa-8924d70f1bbe_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_CurrentFiscalYearEndDate"/>
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    <link:label id="lab_dgii_IoTProductsandServicesMember_7178db30-be57-41c6-b567-abcfd4a2ee9c_terseLabel_en-US" xlink:label="lab_dgii_IoTProductsandServicesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">IoT Products &amp; Services</link:label>
    <link:label id="lab_dgii_IoTProductsandServicesMember_e6e54758-367f-4e3b-a2b9-67e583c3e537_verboseLabel_en-US" xlink:label="lab_dgii_IoTProductsandServicesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">IoT Products and Services</link:label>
    <link:label id="lab_dgii_IoTProductsandServicesMember_label_en-US" xlink:label="lab_dgii_IoTProductsandServicesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">IoT Products and Services [Member]</link:label>
    <link:label id="lab_dgii_IoTProductsandServicesMember_documentation_en-US" xlink:label="lab_dgii_IoTProductsandServicesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">IoT Products &amp; Services [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dgii_IoTProductsandServicesMember" xlink:href="dgii-20220930.xsd#dgii_IoTProductsandServicesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dgii_IoTProductsandServicesMember" xlink:to="lab_dgii_IoTProductsandServicesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dgii_A2022Member_0f58a30c-b3d7-4b0f-bfce-a5a9c6b55edb_terseLabel_en-US" xlink:label="lab_dgii_A2022Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2022</link:label>
    <link:label id="lab_dgii_A2022Member_label_en-US" xlink:label="lab_dgii_A2022Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2022 [Member]</link:label>
    <link:label id="lab_dgii_A2022Member_documentation_en-US" xlink:label="lab_dgii_A2022Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2022</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dgii_A2022Member" xlink:href="dgii-20220930.xsd#dgii_A2022Member"/>
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    <link:label id="lab_us-gaap_StatementTable_600fa9b7-1bc8-44bc-81aa-3aceb4321d22_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_StatementTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementTable" xlink:to="lab_us-gaap_StatementTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_065ad9ce-19e4-4315-8bfd-702fa5a91500_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Recent Accounting Developments</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
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    <link:label id="lab_srt_RangeAxis_33aa79b3-25d2-43ed-96d0-55c585f9424e_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
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    <link:label id="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy_7a9ef6f7-7ae5-448a-a1c0-7cb3902ed452_terseLabel_en-US" xlink:label="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounts Receivable</link:label>
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    <link:label id="lab_srt_NorthAmericaMember_fb691c98-5195-4c43-a9a7-a769f273b7a4_terseLabel_en-US" xlink:label="lab_srt_NorthAmericaMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">North America, primarily United States</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_srt_NorthAmericaMember" xlink:href="https://xbrl.fasb.org/srt/2021/elts/srt-2021-01-31.xsd#srt_NorthAmericaMember"/>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsForeign_0d5df571-f3d4-4375-9a05-80e4f41f17db_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsForeign" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Non-U.S. operating losses</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfGoodwillTextBlock_0c97d6a7-7ad0-45ad-9fb4-2bd52ebc3ba7_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Changes in Carrying Amount of Goodwill</link:label>
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    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedContingentLiability_1e5fea27-6295-4b83-abdf-b22397fba2a8_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedContingentLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Contingent Liability</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedContingentLiability_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedContingentLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Contingent Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedContingentLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedContingentLiability"/>
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    <link:label id="lab_dgii_The2020PlanMember_4daade9d-78e5-4c7b-82e5-4227f545b5ea_terseLabel_en-US" xlink:label="lab_dgii_The2020PlanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The 2020 Plan</link:label>
    <link:label id="lab_dgii_The2020PlanMember_label_en-US" xlink:label="lab_dgii_The2020PlanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The 2020 Plan [Member]</link:label>
    <link:label id="lab_dgii_The2020PlanMember_documentation_en-US" xlink:label="lab_dgii_The2020PlanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The 2020 Plan</link:label>
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    <link:label id="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent_6867c31b-1768-46e6-9ac2-bb00fdd1c444_verboseLabel_en-US" xlink:label="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accrued compensation</link:label>
    <link:label id="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Employee-related Liabilities, Current</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:to="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_50bcf09d-1a73-4432-9356-f5849e936195_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Statement Location [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_5a637d8b-2232-45e0-83ff-4d1574b0f143_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Employee Service Share-based Compensation, Allocation of Recognized Period Costs, by Report Line [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_label_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Statement Location [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_IncomeStatementLocationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementLocationAxis" xlink:to="lab_us-gaap_IncomeStatementLocationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_79a7838f-5f8a-465c-881d-64e42339aaaa_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated amortization</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finite-Lived Intangible Assets, Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_378fb5b0-240e-4b7b-8733-6a608b6a44da_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2021/elts/srt-2021-01-31.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock_152d8c43-451a-4730-b14a-09ef20a3c33b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfMaturitiesOfLongTermDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Maturities of Long-term Debt [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_LeaseholdImprovementsGross_fd56f1b7-0a3a-45b4-a9df-84d7352f5450_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseholdImprovementsGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Leasehold Improvements, Gross</link:label>
    <link:label id="lab_us-gaap_LeaseholdImprovementsGross_label_en-US" xlink:label="lab_us-gaap_LeaseholdImprovementsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Leasehold Improvements, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseholdImprovementsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_LeaseholdImprovementsGross"/>
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    <link:label id="lab_dei_EntityIncorporationStateCountryCode_9dc9872c-c9ac-49ca-a1e0-b7567e4b8115_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
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    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerAbstract_185e4686-b492-4ad0-a4cd-3a65fff918d3_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue from Contract with Customer [Abstract]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_RevenueFromContractWithCustomerAbstract"/>
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    <link:label id="lab_us-gaap_AdditionalPaidInCapitalCommonStock_d621afda-b1d0-4810-8bb0-4a9dd9f839f9_verboseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalCommonStock_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Additional Paid in Capital, Common Stock</link:label>
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    <link:label id="lab_us-gaap_RestructuringCostAndReserveAxis_da6adc13-2e99-418a-ae67-727f1cab9d72_terseLabel_en-US" xlink:label="lab_us-gaap_RestructuringCostAndReserveAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restructuring Type [Axis]</link:label>
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    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_0b6982f0-e6d4-4239-9311-e8364f92a6cd_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other non-current assets</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsNoncurrent" xlink:to="lab_us-gaap_OtherAssetsNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dgii_SwinglineSubfacilityMember_0cf8f1a3-6d10-4865-8348-3f2bea408dab_terseLabel_en-US" xlink:label="lab_dgii_SwinglineSubfacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Swingline Subfacility</link:label>
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    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_df48f6a0-44c5-4991-9e01-778e2a002c76_terseLabel_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segments [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:to="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_710ca7be-5488-46ad-b3bf-5ac4f6a09824_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Expected dividend yield</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Expected Dividend Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CompensationAndRetirementDisclosureAbstract_ee0cac1b-9d15-4db5-9eb2-59f2e299597c_terseLabel_en-US" xlink:label="lab_us-gaap_CompensationAndRetirementDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Retirement Benefits [Abstract]</link:label>
    <link:label id="lab_us-gaap_CompensationAndRetirementDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CompensationAndRetirementDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Retirement Benefits [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CompensationAndRetirementDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_CompensationAndRetirementDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CompensationAndRetirementDisclosureAbstract" xlink:to="lab_us-gaap_CompensationAndRetirementDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFileNumber_ff701dff-0a59-4803-9733-b85a12ac864f_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity File Number</link:label>
    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity File Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_EntityFileNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFileNumber" xlink:to="lab_dei_EntityFileNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_bdedf5e6-dee1-4518-88ea-df9687956059_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stock-based compensation expense</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">APIC, Share-based Payment Arrangement, Increase for Cost Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:to="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod_87b30c19-c000-4f41-87f8-508989c7db19_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Options Outstanding, Forfeited / Cancelled</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Options, Forfeitures and Expirations in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ValuationAndQualifyingAccountsDisclosureLineItems_3ed710a4-9273-4b64-adf9-354fcfe52e33_terseLabel_en-US" xlink:label="lab_srt_ValuationAndQualifyingAccountsDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">SEC Schedule, 12-09, Valuation and Qualifying Accounts Disclosure [Line Items]</link:label>
    <link:label id="lab_srt_ValuationAndQualifyingAccountsDisclosureLineItems_label_en-US" xlink:label="lab_srt_ValuationAndQualifyingAccountsDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">SEC Schedule, 12-09, Valuation and Qualifying Accounts Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ValuationAndQualifyingAccountsDisclosureLineItems" xlink:href="https://xbrl.fasb.org/srt/2021/elts/srt-2021-01-31.xsd#srt_ValuationAndQualifyingAccountsDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ValuationAndQualifyingAccountsDisclosureLineItems" xlink:to="lab_srt_ValuationAndQualifyingAccountsDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_dgii_PriorCreditFacilityMember_a2469e8d-e70a-463e-8559-0561613efc48_terseLabel_en-US" xlink:label="lab_dgii_PriorCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Prior Credit Facility</link:label>
    <link:label id="lab_dgii_PriorCreditFacilityMember_label_en-US" xlink:label="lab_dgii_PriorCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Prior Credit Facility [Member]</link:label>
    <link:label id="lab_dgii_PriorCreditFacilityMember_documentation_en-US" xlink:label="lab_dgii_PriorCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Prior Credit Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dgii_PriorCreditFacilityMember" xlink:href="dgii-20220930.xsd#dgii_PriorCreditFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dgii_PriorCreditFacilityMember" xlink:to="lab_dgii_PriorCreditFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dgii_ExercisePriceRangeOneMember_8229db6f-a80d-41d7-851b-f472855b24c0_terseLabel_en-US" xlink:label="lab_dgii_ExercisePriceRangeOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">$7.40 - $9.03</link:label>
    <link:label id="lab_dgii_ExercisePriceRangeOneMember_label_en-US" xlink:label="lab_dgii_ExercisePriceRangeOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Exercise Price Range One [Member]</link:label>
    <link:label id="lab_dgii_ExercisePriceRangeOneMember_documentation_en-US" xlink:label="lab_dgii_ExercisePriceRangeOneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Exercise Price Range One [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dgii_ExercisePriceRangeOneMember" xlink:href="dgii-20220930.xsd#dgii_ExercisePriceRangeOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dgii_ExercisePriceRangeOneMember" xlink:to="lab_dgii_ExercisePriceRangeOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableLeaseCost_33ed7236-7a87-4830-bd2f-e33194ba8139_terseLabel_en-US" xlink:label="lab_us-gaap_VariableLeaseCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Variable lease cost</link:label>
    <link:label id="lab_us-gaap_VariableLeaseCost_label_en-US" xlink:label="lab_us-gaap_VariableLeaseCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Variable Lease, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableLeaseCost" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_VariableLeaseCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableLeaseCost" xlink:to="lab_us-gaap_VariableLeaseCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_0771f576-eea0-449f-91b1-273aa0b23d9c_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liability Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liability Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByLiabilityClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_FairValueByLiabilityClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByLiabilityClassAxis" xlink:to="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BuildingMember_abd3b70f-2072-4ce3-bb19-9b826dea943d_terseLabel_en-US" xlink:label="lab_us-gaap_BuildingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Building Improvements and buildings</link:label>
    <link:label id="lab_us-gaap_BuildingMember_e90f4df6-8247-40aa-93fc-7420dc4a497f_verboseLabel_en-US" xlink:label="lab_us-gaap_BuildingMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Buildings</link:label>
    <link:label id="lab_us-gaap_BuildingMember_label_en-US" xlink:label="lab_us-gaap_BuildingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Building [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BuildingMember" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_BuildingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BuildingMember" xlink:to="lab_us-gaap_BuildingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_694cc86c-4e20-4944-a2bc-3da7433f6438_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restricted Stock Units, Weighted Average Grant Date Fair Value per Common Share, Granted</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain_8220b064-a247-4a9b-95cf-a9d2b1f6771c_terseLabel_en-US" xlink:label="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Title of Individual [Domain]</link:label>
    <link:label id="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain_label_en-US" xlink:label="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Title of Individual [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:href="https://xbrl.fasb.org/srt/2021/elts/srt-2021-01-31.xsd#srt_TitleOfIndividualWithRelationshipToEntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:to="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dgii_ExercisePriceRangeFiveMember_0b58a016-5dcf-4e18-af66-6506da356be3_terseLabel_en-US" xlink:label="lab_dgii_ExercisePriceRangeFiveMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">$12.64 - $13.92</link:label>
    <link:label id="lab_dgii_ExercisePriceRangeFiveMember_label_en-US" xlink:label="lab_dgii_ExercisePriceRangeFiveMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Exercise Price Range Five [Member]</link:label>
    <link:label id="lab_dgii_ExercisePriceRangeFiveMember_documentation_en-US" xlink:label="lab_dgii_ExercisePriceRangeFiveMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Exercise Price Range Five [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dgii_ExercisePriceRangeFiveMember" xlink:href="dgii-20220930.xsd#dgii_ExercisePriceRangeFiveMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dgii_ExercisePriceRangeFiveMember" xlink:to="lab_dgii_ExercisePriceRangeFiveMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis_fac7d6d2-51bf-48d8-8d18-cfd9591b8323_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Exercise Price Range [Axis]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Exercise Price Range [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis" xlink:to="lab_us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityDomain_87389c32-9b2a-48a7-8684-40c55fd366b4_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityDomain_label_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_CreditFacilityDomain"/>
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    <link:label id="lab_us-gaap_InventoryNetAbstract_eac968ff-f420-4f01-a63d-6c5330411922_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventories:</link:label>
    <link:label id="lab_us-gaap_InventoryNetAbstract_label_en-US" xlink:label="lab_us-gaap_InventoryNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventory, Net [Abstract]</link:label>
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    <link:label id="lab_us-gaap_GoodwillAcquiredDuringPeriod_6e0f08c9-76c1-4da0-b4f8-073e466d3164_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAcquiredDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Acquisition</link:label>
    <link:label id="lab_us-gaap_GoodwillAcquiredDuringPeriod_label_en-US" xlink:label="lab_us-gaap_GoodwillAcquiredDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Goodwill, Acquired During Period</link:label>
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    <link:label id="lab_us-gaap_PerformanceSharesMember_4a4790f8-8079-4f67-a51a-db8cd6bf1df6_terseLabel_en-US" xlink:label="lab_us-gaap_PerformanceSharesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Performance Shares</link:label>
    <link:label id="lab_us-gaap_PerformanceSharesMember_label_en-US" xlink:label="lab_us-gaap_PerformanceSharesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Performance Shares [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PerformanceSharesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PerformanceSharesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PerformanceSharesMember" xlink:to="lab_us-gaap_PerformanceSharesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_239f2457-216d-4806-b612-89f4efbf1207_verboseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commitments and Contingencies (see Note 16)</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingencies" xlink:to="lab_us-gaap_CommitmentsAndContingencies" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_9b41383f-8e51-407c-912c-24c98a06d374_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated other comprehensive loss</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_17e31280-4dd9-481d-a333-1db275527bf8_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_dgii_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfContinuousDaysOfService_be6bb9ed-b74d-460c-9e5d-d54e78a6d5f9_terseLabel_en-US" xlink:label="lab_dgii_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfContinuousDaysOfService" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of continuous days of service</link:label>
    <link:label id="lab_dgii_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfContinuousDaysOfService_label_en-US" xlink:label="lab_dgii_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfContinuousDaysOfService" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Number of Continuous Days of Service</link:label>
    <link:label id="lab_dgii_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfContinuousDaysOfService_documentation_en-US" xlink:label="lab_dgii_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfContinuousDaysOfService" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Number of Continuous Days of Service</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dgii_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfContinuousDaysOfService" xlink:href="dgii-20220930.xsd#dgii_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfContinuousDaysOfService"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dgii_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfContinuousDaysOfService" xlink:to="lab_dgii_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfContinuousDaysOfService" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_96e71787-77d3-46a1-8ca4-9ea15e6d3399_terseLabel_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Less allowance for doubtful accounts</link:label>
    <link:label id="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent_label_en-US" xlink:label="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounts Receivable, Allowance for Credit Loss, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:to="lab_us-gaap_AllowanceForDoubtfulAccountsReceivableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryWriteDown_80321b01-6a69-452f-bb25-49c2dcdfd766_verboseLabel_en-US" xlink:label="lab_us-gaap_InventoryWriteDown" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Provision for inventory obsolescence</link:label>
    <link:label id="lab_us-gaap_InventoryWriteDown_label_en-US" xlink:label="lab_us-gaap_InventoryWriteDown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventory Write-down</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryWriteDown" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_InventoryWriteDown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryWriteDown" xlink:to="lab_us-gaap_InventoryWriteDown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedIncomeTaxesNoncurrent_46db17d3-107f-4837-bb04-cb4f99ad1bfb_verboseLabel_en-US" xlink:label="lab_us-gaap_AccruedIncomeTaxesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income taxes payable</link:label>
    <link:label id="lab_us-gaap_AccruedIncomeTaxesNoncurrent_label_en-US" xlink:label="lab_us-gaap_AccruedIncomeTaxesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accrued Income Taxes, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedIncomeTaxesNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_AccruedIncomeTaxesNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedIncomeTaxesNoncurrent" xlink:to="lab_us-gaap_AccruedIncomeTaxesNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfDebtIssuanceCosts_7dd58e73-2c41-45a7-9d57-b956ca64c07e_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments of debt issuance costs</link:label>
    <link:label id="lab_us-gaap_PaymentsOfDebtIssuanceCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_PaymentsOfDebtIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:to="lab_us-gaap_PaymentsOfDebtIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AuditorName_328c9b6c-9170-453d-b526-c1d9d9a9b03f_terseLabel_en-US" xlink:label="lab_dei_AuditorName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Auditor Name</link:label>
    <link:label id="lab_dei_AuditorName_label_en-US" xlink:label="lab_dei_AuditorName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Auditor Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorName" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_AuditorName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AuditorName" xlink:to="lab_dei_AuditorName" xlink:type="arc" order="1"/>
    <link:label id="lab_dgii_OEMSolutionsMember_618e603e-94ea-496d-a838-89843f2cc45b_terseLabel_en-US" xlink:label="lab_dgii_OEMSolutionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">OEM Solutions</link:label>
    <link:label id="lab_dgii_OEMSolutionsMember_label_en-US" xlink:label="lab_dgii_OEMSolutionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">OEM Solutions [Member]</link:label>
    <link:label id="lab_dgii_OEMSolutionsMember_documentation_en-US" xlink:label="lab_dgii_OEMSolutionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">OEM Solutions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dgii_OEMSolutionsMember" xlink:href="dgii-20220930.xsd#dgii_OEMSolutionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dgii_OEMSolutionsMember" xlink:to="lab_dgii_OEMSolutionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems_9c38119d-6e78-42d3-8e0f-69606af5382c_terseLabel_en-US" xlink:label="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenues from External Customers and Long-Lived Assets [Line Items]</link:label>
    <link:label id="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenues from External Customers and Long-Lived Assets [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:to="lab_us-gaap_RevenuesFromExternalCustomersAndLongLivedAssetsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_9e36759a-1279-4311-a488-a4e31405870a_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash Equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_CashAndCashEquivalentsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:to="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockShares_5e88ddf0-c7b6-4ba3-9f8e-5d0c4467b06c_verboseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockShares" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Treasury stock, shares</link:label>
    <link:label id="lab_us-gaap_TreasuryStockShares_label_en-US" xlink:label="lab_us-gaap_TreasuryStockShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Treasury Stock, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockShares" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_TreasuryStockShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockShares" xlink:to="lab_us-gaap_TreasuryStockShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_305e665a-87ad-4910-a263-0f1759a1eadc_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Less imputed interest</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount"/>
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    <link:label id="lab_us-gaap_SellingAndMarketingExpense_acf91027-67b7-4132-8622-bf543692ae27_verboseLabel_en-US" xlink:label="lab_us-gaap_SellingAndMarketingExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sales and marketing</link:label>
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    <link:label id="lab_dgii_ThePurchasePlanMember_c5a74169-9b50-4375-b231-7921ded2cd55_terseLabel_en-US" xlink:label="lab_dgii_ThePurchasePlanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">The Purchase Plan</link:label>
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    <link:label id="lab_us-gaap_StatementLineItems_9492793c-f6c8-40df-b0cb-f7c56268fe52_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement [Line Items]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationAllowancesAndReservesDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ValuationAllowancesAndReservesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationAllowancesAndReservesDomain" xlink:to="lab_us-gaap_ValuationAllowancesAndReservesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProvisionForOtherCreditLosses_5b4d894f-e1b5-4bc9-b85e-e7dc8a017844_terseLabel_en-US" xlink:label="lab_us-gaap_ProvisionForOtherCreditLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Additions</link:label>
    <link:label id="lab_us-gaap_ProvisionForOtherCreditLosses_label_en-US" xlink:label="lab_us-gaap_ProvisionForOtherCreditLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Provision for Other Credit Losses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProvisionForOtherCreditLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ProvisionForOtherCreditLosses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProvisionForOtherCreditLosses" xlink:to="lab_us-gaap_ProvisionForOtherCreditLosses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_28120e86-421b-4947-b16a-6a0f28bf7695_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Weighted Average Exercise Price [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Exercise Price [Abstract]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_706bc1a6-80a2-405b-96e9-a0fd5b377db0_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Issuance of stock under stock award plans</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Shares Issued, Value, Share-based Payment Arrangement, after Forfeiture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetirementPlanTypeDomain_ee69b2c7-4aa4-4842-95db-7bb0fa86275e_terseLabel_en-US" xlink:label="lab_us-gaap_RetirementPlanTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Retirement Plan Type [Domain]</link:label>
    <link:label id="lab_us-gaap_RetirementPlanTypeDomain_label_en-US" xlink:label="lab_us-gaap_RetirementPlanTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Retirement Plan Type [Domain]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetirementPlanTypeDomain" xlink:to="lab_us-gaap_RetirementPlanTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DomesticCountryMember_31ffc118-4bcf-427e-ae02-54ecef14ed0d_terseLabel_en-US" xlink:label="lab_us-gaap_DomesticCountryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">United States Federal Tax Jurisdiction</link:label>
    <link:label id="lab_us-gaap_DomesticCountryMember_label_en-US" xlink:label="lab_us-gaap_DomesticCountryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Domestic Tax Authority [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DomesticCountryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DomesticCountryMember"/>
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    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsRangeOfOutcomesValueHigh_0170e1e7-8628-48a7-8f31-9190bd69754e_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsRangeOfOutcomesValueHigh" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Earn-out payment maximum</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsRangeOfOutcomesValueHigh_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsRangeOfOutcomesValueHigh" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Combination, Contingent Consideration Arrangements, Range of Outcomes, Value, High</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationContingentConsiderationArrangementsRangeOfOutcomesValueHigh" xlink:to="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsRangeOfOutcomesValueHigh" xlink:type="arc" order="1"/>
    <link:label id="lab_dgii_ExercisePriceRangeFourMember_70cb4ad7-95c6-45b9-8b7a-b95fc51ab9d9_terseLabel_en-US" xlink:label="lab_dgii_ExercisePriceRangeFourMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">$11.24 - $12.63</link:label>
    <link:label id="lab_dgii_ExercisePriceRangeFourMember_label_en-US" xlink:label="lab_dgii_ExercisePriceRangeFourMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Exercise Price Range Four [Member]</link:label>
    <link:label id="lab_dgii_ExercisePriceRangeFourMember_documentation_en-US" xlink:label="lab_dgii_ExercisePriceRangeFourMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Exercise Price Range Four [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dgii_ExercisePriceRangeFourMember" xlink:href="dgii-20220930.xsd#dgii_ExercisePriceRangeFourMember"/>
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    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
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    <link:label id="lab_us-gaap_TaxPeriodAxis_aaf11a1a-7b06-4329-acaa-9abb2d216444_terseLabel_en-US" xlink:label="lab_us-gaap_TaxPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tax Period [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TaxPeriodAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_TaxPeriodAxis"/>
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    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent_6a5bbbe6-b135-40d4-be26-aac30f40b64b_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Percent of market value</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Purchase Price of Common Stock, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_dgii_OtherIncomeNet_869b0944-45d8-41af-af0c-21f0d198b167_totalLabel_en-US" xlink:label="lab_dgii_OtherIncomeNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total other expense, net</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_17e04c8f-3664-42f2-ab38-32a322ea564f_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property, Plant and Equipment, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Long-Lived Tangible Asset [Axis]</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsValuationAllowance_87a4a690-6894-4eda-bc9b-e0b9d6b76158_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Valuation allowance</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsValuationAllowance_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Deferred Tax Assets, Valuation Allowance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_DeferredTaxAssetsValuationAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:to="lab_us-gaap_DeferredTaxAssetsValuationAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_dgii_ExercisePriceRangeSixMember_6013121e-141c-4655-89bc-f1392fc7038e_terseLabel_en-US" xlink:label="lab_dgii_ExercisePriceRangeSixMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">$13.93 - $17.94</link:label>
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    <link:label id="lab_us-gaap_RestructuringCostAndReserveLineItems_4abbb015-32b0-48af-aceb-583b48f5e9ad_terseLabel_en-US" xlink:label="lab_us-gaap_RestructuringCostAndReserveLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restructuring Cost and Reserve [Line Items]</link:label>
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    <link:label id="lab_us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock_ac23c892-e31b-4b89-84b4-4a9329283a03_terseLabel_en-US" xlink:label="lab_us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">EMPLOYEE BENEFIT PLANS</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_a746164f-2735-42c0-b40b-d9c8e2ad6261_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Options Outstanding, Granted</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross"/>
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    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_2e560084-08e2-4457-b3c5-51125440f382_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Business Acquisitions, by Acquisition [Table]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:to="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByAssetClassAxis_b568c3cb-cd16-4a36-ab18-99eea17d3737_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByAssetClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByAssetClassAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByAssetClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByAssetClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2021/elts/us-gaap-2021-01-31.xsd#us-gaap_FairValueByAssetClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByAssetClassAxis" xlink:to="lab_us-gaap_FairValueByAssetClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentAnnualReport_81368234-17d5-4c65-b9de-dfe9a1ba1292_terseLabel_en-US" xlink:label="lab_dei_DocumentAnnualReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Annual Report</link:label>
    <link:label id="lab_dei_DocumentAnnualReport_label_en-US" xlink:label="lab_dei_DocumentAnnualReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Annual Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentAnnualReport" xlink:href="https://xbrl.sec.gov/dei/2021q4/dei-2021q4.xsd#dei_DocumentAnnualReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentAnnualReport" xlink:to="lab_dei_DocumentAnnualReport" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScenarioForecastMember_029c0f44-920c-4483-a584-71ab5c1f5491_terseLabel_en-US" xlink:label="lab_srt_ScenarioForecastMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Forecast</link:label>
    <link:label id="lab_srt_ScenarioForecastMember_label_en-US" xlink:label="lab_srt_ScenarioForecastMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Forecast [Member]</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsDeferredRent_eccb3ab5-8840-4ec0-9463-60234f2f0b89_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsDeferredRent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Lease liability</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_7110ad1e-9946-4390-a5be-30abb5f9e4fc_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from issuances of stock, net of offering expenses</link:label>
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    <link:label id="lab_us-gaap_Assets_963fe545-4cb4-48a6-8be4-a0654cb8e9db_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total assets</link:label>
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    <link:label id="lab_us-gaap_PlanNameDomain_4d7caa8f-2381-4013-b550-ddf9e7f6fc38_terseLabel_en-US" xlink:label="lab_us-gaap_PlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Plan Name [Domain]</link:label>
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    <link:label id="lab_srt_DirectorMember_c0a810a8-8f73-40b7-9488-4055da59fcc6_terseLabel_en-US" xlink:label="lab_srt_DirectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Director</link:label>
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    <link:label id="lab_us-gaap_InterestPaidNet_6b042216-ed44-4544-a76a-a4ae2a246c5c_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest paid</link:label>
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    <link:label id="lab_us-gaap_OtherNoncurrentLiabilitiesMember_8768cff4-f3f1-4ce6-947a-768a22f3f649_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNoncurrentLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Noncurrent income taxes payable</link:label>
    <link:label id="lab_us-gaap_OtherNoncurrentLiabilitiesMember_label_en-US" xlink:label="lab_us-gaap_OtherNoncurrentLiabilitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Noncurrent Liabilities [Member]</link:label>
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    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_8c66d4fc-3742-4dac-a9a7-f85b76f14edb_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Acquisition, Acquiree [Domain]</link:label>
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    <link:label id="lab_dgii_FullEmployerMatchMember_c10863f5-fe30-47f7-84d2-5cad474a7431_terseLabel_en-US" xlink:label="lab_dgii_FullEmployerMatchMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Full Employer Match</link:label>
    <link:label id="lab_dgii_FullEmployerMatchMember_label_en-US" xlink:label="lab_dgii_FullEmployerMatchMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Full Employer Match [Member]</link:label>
    <link:label id="lab_dgii_FullEmployerMatchMember_documentation_en-US" xlink:label="lab_dgii_FullEmployerMatchMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Full Employer Match [Member]</link:label>
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    <link:label id="lab_us-gaap_CostOfGoodsAndServicesSold_e37def19-3dd7-42d4-9cc3-aeff56f08ade_totalLabel_en-US" xlink:label="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total cost of sales</link:label>
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    <link:label id="lab_us-gaap_RestructuringAndRelatedActivitiesAbstract_19258000-088d-4098-9a82-fd0455ead52c_terseLabel_en-US" xlink:label="lab_us-gaap_RestructuringAndRelatedActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restructuring and Related Activities [Abstract]</link:label>
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    <link:label id="lab_us-gaap_AccountsReceivableNetCurrentAbstract_daf85e25-4b71-4c41-813f-8edf8ee12940_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounts receivable, net:</link:label>
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    <link:label id="lab_dei_EntityCentralIndexKey_f8d9e6f4-4a19-463f-9338-20c97e914bbf_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Central Index Key</link:label>
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    <link:label id="lab_us-gaap_LeaseCost_02b4bea8-5aad-4472-b9a2-36316b2b9e1d_totalLabel_en-US" xlink:label="lab_us-gaap_LeaseCost" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total lease cost</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeUpperRangeLimit_86f588f3-8022-452e-b11d-37a81f86b1f5_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeUpperRangeLimit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Exercise Price Range, Upper Range</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeUpperRangeLimit_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansExercisePriceRangeUpperRangeLimit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-based Payment Arrangement, Option, Exercise Price Range, Upper Range Limit</link:label>
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    <link:label id="lab_us-gaap_CustomerRelationshipsMember_0db0f24c-4f8c-4f58-a5b1-d7df994c2c28_terseLabel_en-US" xlink:label="lab_us-gaap_CustomerRelationshipsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Customer Relationships</link:label>
    <link:label id="lab_us-gaap_CustomerRelationshipsMember_label_en-US" xlink:label="lab_us-gaap_CustomerRelationshipsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Customer Relationships [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CustomerRelationshipsMember" xlink:to="lab_us-gaap_CustomerRelationshipsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dgii_EffectiveIncomeTaxRateReconciliationGILTI_7cb6a351-d05e-432e-9f4a-a902479fb150_terseLabel_en-US" xlink:label="lab_dgii_EffectiveIncomeTaxRateReconciliationGILTI" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Global intangible low-taxed income</link:label>
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    <link:label id="lab_us-gaap_LossContingenciesLineItems_f5bc49fd-884e-4117-9311-405362d6c433_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingenciesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Loss Contingencies [Line Items]</link:label>
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    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_42e4a02a-62d2-49f7-baa2-2d419268d9e2_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other non-current liabilities</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesNoncurrent" xlink:to="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dgii_SubscriberassetsMember_0889a50a-cc00-4eb6-ab32-1614a6c3dc5f_terseLabel_en-US" xlink:label="lab_dgii_SubscriberassetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subscriber assets</link:label>
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    <link:label id="lab_dgii_SubscriberassetsMember_documentation_en-US" xlink:label="lab_dgii_SubscriberassetsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subscriber assets [Member]</link:label>
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    <link:label id="lab_us-gaap_LineOfCreditFacilityTable_c285c4d0-e024-4c25-9916-d0f1a26707a4_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Line of Credit Facility [Table]</link:label>
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