Modularity-Fair Deep Community Detection with Multi-valued Sensitive Attributes

Modularity-Fair Deep Community Detection with Multi-valued Sensitive Attributes | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Modularity-Fair Deep Community Detection with Multi-valued Sensitive Attributes Christos Gkartzios, Evaggelia Pitoura, Panayiotis Tsaparas This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8474880/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract Detecting meaningful communities in networks is essential for understanding complex social, biological, and information systems. Modularity effectively captures the quality of communities by comparing the observed and expected edge densities, but it often overlooks fairness with regards to the connectivity of different groups of nodes within the communities. In this work, we address this limitation by proposing fairness-aware community detection algorithms that incorporate group-sensitive connectivity into the modularity framework. Our approach is based on optimizing distinct sub-matrices of the modularity matrix that isolate intra-group and inter-group connections. We introduce two algorith-mic families: (a) Input-based methods, including fair spectral and deep learning algorithms that directly operate on these sub-matrices; and (b) Loss-based methods , which integrate fairness-aware sub-matrix information into the learning objective of deep community detection models. The proposed approach is applicable to both binary and multi-valued sensitive attributes. Our experiments on synthetic and real-world networks demonstrate that our algorithms significantly improve group connectivity fairness with controlled trade-offs in modularity. Community Detection Spectral Clustering Deep Clustering Social Networks Fairness-aware community detection Graph Neural Networks Group Modularity Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 01 Apr, 2026 Reviewers agreed at journal 20 Mar, 2026 Reviewers agreed at journal 19 Mar, 2026 Reviewers invited by journal 15 Mar, 2026 Editor assigned by journal 18 Jan, 2026 Submission checks completed at journal 29 Dec, 2025 First submitted to journal 29 Dec, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8474880","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":606543305,"identity":"9035cf8d-4474-4061-9ccd-ee1deaf72f82","order_by":0,"name":"Christos Gkartzios","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA30lEQVRIiWNgGAWjYDACCQjFw8DAfADMYiNOSwJIC1sCaVpAFhkQ5y7+2e0XP1f+qJPh5z/z8eMPhsNyfAzs1z7gteTOmWLJMwlsPJIzcjdL8zAcNmZj4CmegU+LgUROgmRDAg+PwQ3ebcwMDIcT2xh4kvE6DKgl+WdDggSPwfkzzxh/EKcl/RjQFgMegwM5QCeBtbAfxqtF4kYOm2VDWgLQL2nG0jwG6cZszDzMeLXwz0h/fLPBps6en//ww48/Kqzl5NvbH+PVghYdIDYzwQhif0BYZBSMglEwCkY2AAA1VT2ecOHNoQAAAABJRU5ErkJggg==","orcid":"","institution":"University of Ioannina","correspondingAuthor":true,"prefix":"","firstName":"Christos","middleName":"","lastName":"Gkartzios","suffix":""},{"id":606543306,"identity":"1b70c8b8-c621-47fa-b2d1-596701a55254","order_by":1,"name":"Evaggelia Pitoura","email":"","orcid":"","institution":"University of Ioannina","correspondingAuthor":false,"prefix":"","firstName":"Evaggelia","middleName":"","lastName":"Pitoura","suffix":""},{"id":606543307,"identity":"32a72ada-a7a1-4b6d-872a-ab8346bcb1c4","order_by":2,"name":"Panayiotis Tsaparas","email":"","orcid":"","institution":"University of Ioannina","correspondingAuthor":false,"prefix":"","firstName":"Panayiotis","middleName":"","lastName":"Tsaparas","suffix":""}],"badges":[],"createdAt":"2025-12-29 17:08:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8474880/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8474880/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105033792,"identity":"ca657d73-deee-4c83-82b6-eebb10d8f807","added_by":"auto","created_at":"2026-03-20 07:21:43","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":757205,"visible":true,"origin":"","legend":"","description":"","filename":"ICDMDeepModularityKAISExtensionNew.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8474880/v1_covered_dd545364-7f04-4a91-8d2a-00d208436508.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Modularity-Fair Deep Community Detection with Multi-valued Sensitive Attributes","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"knowledge-and-information-systems","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"kais","sideBox":"Learn more about [Knowledge and Information Systems](http://link.springer.com/journal/10115)","snPcode":"10115","submissionUrl":"https://submission.nature.com/new-submission/10115/3","title":"Knowledge and Information Systems","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Community Detection, Spectral Clustering, Deep Clustering, Social Networks, Fairness-aware community detection, Graph Neural Networks, Group Modularity","lastPublishedDoi":"10.21203/rs.3.rs-8474880/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8474880/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Detecting meaningful communities in networks is essential for understanding complex social, biological, and information systems. 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