Graph Convolutional Networks: A Critical Review

Graph Convolutional Networks: A Critical Review | 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 Graph Convolutional Networks: A Critical Review Aabid A. Mir, Megat F. Zuhairi, Ahmed Alrehaili, Ali Tufail, Abdallah Namoun This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8677237/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract Graph convolutional networks (GCNs) extend deep learning to graph-structured data using spectral graph theory and spatial message passing. Despite their success, their mathematical foundations remain fragmented. This review mathematically analyzes GCNs by focusing on architecture, theoretical foundations, and fundamental limitations. We propose a unified perspective on graph convolutions by analyzing when spectral filtering and spatial aggregation coincide or diverge, thereby clarifying how convolution can be rigorously defined on irregular graph domains. A central theme is the expressive power of GCNs, which is formulated through the lens of the Weisfeiler–Lehman test and the structural bottlenecks it imposes on graph discrimination. We examine over-smoothing by characterizing how repeated message passing leads to representational collapse, and we complement these analyses with visualizations of entropy loss in node embeddings as depth increases. In addition, we review recent theoretical results on the optimization landscape and convergence behavior of GCN training, highlighting how depth, normalization, and regularization influence trainability. The review further addresses GCN generalization by analyzing theoretical guarantees and failure modes under structural distribution shifts, random perturbations, and adversarial noise. The assessment includes an in-depth spectral analysis of perturbation sensitivity and its relation to the eigenvalue spectrum of the graph Laplacian. The findings highlight that GCNs suffer from limited expressivity and generalization under structural shifts and adversarial perturbations. We advocate for future research on expressive and stable architectures via Lipschitz-continuous designs, denoising-based preprocessing, and spectral regularization. This review serves as a resource and a roadmap for advancing theoretical understanding and practical robustness in GCNs. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 29 Mar, 2026 Reviews received at journal 19 Feb, 2026 Reviewers agreed at journal 08 Feb, 2026 Reviewers agreed at journal 08 Feb, 2026 Reviewers invited by journal 06 Feb, 2026 Editor assigned by journal 01 Feb, 2026 Submission checks completed at journal 24 Jan, 2026 First submitted to journal 23 Jan, 2026 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-8677237","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":587884571,"identity":"dda2895f-cd34-448b-b8ce-d3b04fa6e6bc","order_by":0,"name":"Aabid A. Mir","email":"","orcid":"","institution":"Universiti Kuala Lumpur","correspondingAuthor":false,"prefix":"","firstName":"Aabid","middleName":"A.","lastName":"Mir","suffix":""},{"id":587884572,"identity":"de868709-6e26-4cd8-9172-431981755775","order_by":1,"name":"Megat F. 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