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Finding Cliques in Social Networks: A New Distribution-Free Model

Authors Jacob Fox, Tim Roughgarden, C. Seshadhri, Fan Wei, Nicole Wein

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  • Theory of computation → Fixed parameter tractability
Keywords
  • Graph algorithms
  • social networks
  • fixed-parameter tractability

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Abstract

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.

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Jacob Fox, Tim Roughgarden, C. Seshadhri, Fan Wei, and Nicole Wein. Finding Cliques in Social Networks: A New Distribution-Free Model. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 55:1-55:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.ICALP.2018.55

Author Details

Jacob Fox
  • Department of Mathematics, Stanford University, Stanford, CA 94305, USA
Tim Roughgarden
  • Department of Computer Science, Stanford University, Stanford, CA 94305, USA
C. Seshadhri
  • Department of Computer Science, University of California, Santa Cruz, CA 95064, USA
Fan Wei
  • Department of Mathematics, Stanford University, Stanford, CA 94305, USA
Nicole Wein
  • EECS, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Funding

  • Fox, Jacob: Supported by a Packard Fellowship, an NSF Career Award DMS-1352121, and an Alfred P. Sloan Fellowship
  • Roughgarden, Tim: Supported by NSF award CCF-1524062
  • Wein, Nicole: Supported by an NSF Graduate Fellowship

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