Beyond One Solution: a Comprehensive Exploration of Solution Space in Community Detection for Social Networks

Beyond One Solution: a Comprehensive Exploration of Solution Space in Community Detection for Social Networks | 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 Article Beyond One Solution: a Comprehensive Exploration of Solution Space in Community Detection for Social Networks Fabio Morea, Domenico De Stefano This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6578160/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 31 Oct, 2025 Read the published version in Scientific Reports → Version 1 posted 13 You are reading this latest preprint version Abstract This paper investigates the relevance of systematically exploring the solution space produced by commonly used community detection algorithms, emphasizing its role in enhancing the robustness and reliability of results, particularly in complex real-world social networks. Three core challenges are addressed: the multiplicity of solutions, input ordering bias, and the handling of outliers. Input ordering bias—where the outcome of an algorithm is influenced by the sequence in which nodes and edges are processed—can undermine the interpretability of results by introducing artifacts unrelated to the network topol-ogy. Similarly, the presence of outliers-nodes that do not clearly belong to any community—is often overlooked, with many algorithms either ignoring them or forcing them into existing clusters, thereby affecting the resulting partition. To address these limitations, we propose a methodological framework for systematically exploring the solution space across multiple algorithm runs, incorporating a Bayesian model to assess its stability and a taxonomy to classify its structure. This approach enables a deeper understanding of the variability and uncertainty inherent in community detection, paving the way for more accurate, consistent, and interpretable results. Physical sciences/Mathematics and computing/Statistics Physical sciences/Mathematics and computing/Computational science Social network analysis Community detection Outliers Cliques Horizon project networks Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 31 Oct, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 05 Aug, 2025 Reviews received at journal 13 Jul, 2025 Reviews received at journal 12 Jul, 2025 Reviewers agreed at journal 24 Jun, 2025 Reviewers agreed at journal 22 Jun, 2025 Reviewers agreed at journal 22 Jun, 2025 Reviews received at journal 18 Jun, 2025 Reviewers agreed at journal 22 May, 2025 Reviewers invited by journal 20 May, 2025 Editor invited by journal 14 May, 2025 Editor assigned by journal 07 May, 2025 Submission checks completed at journal 06 May, 2025 First submitted to journal 02 May, 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-6578160","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":459421962,"identity":"1ed41e12-e22d-478a-b0ec-13663a3caa72","order_by":0,"name":"Fabio Morea","email":"","orcid":"","institution":"Consorzio per l'AREA di Ricerca Scientifica e Tecnologica di Trieste","correspondingAuthor":false,"prefix":"","firstName":"Fabio","middleName":"","lastName":"Morea","suffix":""},{"id":459421963,"identity":"0552c338-d11a-4ff8-92c1-79f17ab0d31b","order_by":1,"name":"Domenico De Stefano","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3ElEQVRIiWNgGAWjYDCCAwkgUg6ImQ8wMBiAaGK0HGAwBrLYgCwDoB5mQnoQWnhAVhBhDd/x5MOfP1QYyJuz93yTLij4Y8/Azn8ArxbJM8/SJA6cMTDc2XN2m/QMA4PEBkIOM7iRY8ZwsO0P44YbudukeQwMEgj6xeBG/ucPB/8Z2G+4kfMMpMWeCC05DBIHGwwSgVrYQFoYCToM6BcziTPHDJI3nDlmbM1jYJzYxsxsgFcLMMQef6ioMbDdcLz54W2eP3L2/PwHH+C3BgOwkah+FIyCUTAKRgEWAAB7t0TfiMcQUQAAAABJRU5ErkJggg==","orcid":"","institution":"University of Trieste","correspondingAuthor":true,"prefix":"","firstName":"Domenico","middleName":"","lastName":"De Stefano","suffix":""}],"badges":[],"createdAt":"2025-05-02 11:53:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6578160/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6578160/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-22046-7","type":"published","date":"2025-10-31T15:57:46+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":95039970,"identity":"4ea43a87-4a68-4f90-8255-79e5732e132d","added_by":"auto","created_at":"2025-11-03 16:06:44","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1072453,"visible":true,"origin":"","legend":"","description":"","filename":"BeyondOneSolutionSR.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6578160/v1_covered_43b675c3-820f-49df-84e9-eee1680648f0.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Beyond One Solution: a Comprehensive Exploration of Solution Space in Community Detection for Social Networks","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Social network analysis, Community detection, Outliers, Cliques, Horizon project networks","lastPublishedDoi":"10.21203/rs.3.rs-6578160/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6578160/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper investigates the relevance of systematically exploring the solution space produced by commonly used community detection algorithms, emphasizing its role in enhancing the robustness and reliability of results, particularly in complex real-world social networks. 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