Parameter-free community detection by an operator on eigenvectors of the network adjacency matrix

Parameter-free community detection by an operator on eigenvectors of the network adjacency matrix | 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 Parameter-free community detection by an operator on eigenvectors of the network adjacency matrix Lyle Muller, Priya Bucha Jain, Alexandra Busch, Roberto Budzinski, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8311752/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Community detection is an important problem in network science, potentially enabling structure discovery in key datasets. Existing computational algorithms for detecting communities rely on optimization procedures that require prior knowledge on the number of communities or several free parameters that must be manually tuned. Here, we introduce a fully analytical, parameter-free method for detecting communities in weighted, directed networks, using only the eigenspectrum of the network adjacency matrix. This approach includes a new and robust technique for estimating the number of communities. We prove theoretical guarantees for successful community detection in networks with clustered connectivity and demonstrate the robustness of these guarantees through simulations across a range of noise. We then demonstrate how this mathematical construction can inform the design of specific dynamics in networks of nonlinear oscillators. Taken together, these results open a new path for community detection grounded in mathematical operations on the network adjacency matrix and its eigenspectrum, as an alternative to optimization-based algorithms. Physical sciences/Mathematics and computing/Applied mathematics Physical sciences/Physics Full Text Additional Declarations There is NO Competing Interest. Supplementary Files code.zip Code repository supplement.pdf Supplemental Material rs.pdf Reporting Summary Cite Share Download PDF Status: Posted Version 1 posted 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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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-8311752","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":563119927,"identity":"73cb8ac6-c34d-410c-89d3-c68a365e0cc5","order_by":0,"name":"Lyle 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