{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T05:02:13Z","timestamp":1780462933407,"version":"3.54.1"},"reference-count":43,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T00:00:00Z","timestamp":1768953600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Comput. Neurosci."],"abstract":"<jats:p>\n                    Community detection is a crucial task in network research, applicable to social systems, biology, cybersecurity, and knowledge graphs. Recent advancements in graph neural networks (GNNs) have exhibited significant representational capability; yet, they frequently experience instability and erroneous clustering, often referred to as \u201dhallucinations.\u201d These artifacts stem from sensitivity to high-frequency eigenmodes, over-parameterization, and noise amplification, undermining the robustness of learned communities. To mitigate these constraints, we present F\n                    <jats:sup>2<\/jats:sup>\n                    -CommNet, a Fourier\u2013Fractional neural framework that incorporates fractional-order dynamics, spectrum filtering, and Lyapunov-based stability analysis. The fractional operator implements long-memory dampening that mitigates oscillations, whereas Fourier spectral projections selectively attenuate eigenmodes susceptible to hallucination. Theoretical analysis delineates certain stability criteria under Lipschitz non-linearities and constrained disturbances, resulting in a demonstrable expansion of the Lyapunov margin. Experimental validation on synthetic and actual networks indicates that F\n                    <jats:sup>2<\/jats:sup>\n                    -CommNet reliably diminishes hallucination indices, enhances stability margins, and produces interpretable communities in comparison to integer-order GNN baselines. This study integrates fractional calculus, spectral graph theory, and neural network dynamics, providing a systematic method for hallucination-resistant community discovery.\n                  <\/jats:p>","DOI":"10.3389\/fncom.2025.1731452","type":"journal-article","created":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T06:45:00Z","timestamp":1768977900000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["F2-CommNet: Fourier\u2013Fractional neural networks with Lyapunov stability guarantees for hallucination-resistant community detection"],"prefix":"10.3389","volume":"19","author":[{"given":"Daozheng","family":"Qu","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Liverpool","place":["Liverpool, United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanfei","family":"Ma","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Fairleigh Dickinson University","place":["Vancouver, BC, Canada"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1965","published-online":{"date-parts":[[2026,1,21]]},"reference":[{"key":"B1","author":"Abbahaddou","year":"2024"},{"key":"B2","author":"Balcilar","year":"2021"},{"key":"B3","doi-asserted-by":"publisher","first-page":"1518","DOI":"10.1007\/s10618-023-00932-w","article-title":"A graph convolutional fusion model for community detection in multiplex networks","volume":"37","author":"Cai","year":"2023","journal-title":"Data Min. 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