2026-07-24T17:11:57Z https://drops.dagstuhl.de/oai

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Finding Cliques in Social Networks: A New Distribution-Free Model Fox, Jacob Roughgarden, Tim Seshadhri, C. Wei, Fan Wein, Nicole Graph algorithms social networks fixed-parameter tractability We propose a new distribution-free model of social networks. Our definitions are motivated by one of the most universal signatures of social networks, triadic closure - the property that pairs of vertices with common neighbors tend to be adjacent. Our most basic definition is that of a c-closed graph, where for every pair of vertices u,v with at least c common neighbors, u and v are adjacent. We study the classic problem of enumerating all maximal cliques, an important task in social network analysis. We prove that this problem is fixed-parameter tractable with respect to c on c-closed graphs. Our results carry over to weakly c-closed graphs, which only require a vertex deletion ordering that avoids pairs of non-adjacent vertices with c common neighbors. Numerical experiments show that well-studied social networks tend to be weakly c-closed for modest values of c. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Jacob Fox and Tim Roughgarden and C. Seshadhri and Fan Wei and Nicole Wein 2018 Is Part Of LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2018.55 urn:nbn:de:0030-drops-90596 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.55 eng https://creativecommons.org/licenses/by/3.0/legalcode