License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2018.55
URN: urn:nbn:de:0030-drops-90596
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9059/
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Fox, Jacob ; Roughgarden, Tim ; Seshadhri, C. ; Wei, Fan ; Wein, Nicole

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

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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.

BibTeX - Entry

@InProceedings{fox_et_al:LIPIcs:2018:9059,
  author =	{Jacob Fox and Tim Roughgarden and C. Seshadhri and Fan Wei and Nicole Wein},
  title =	{{Finding Cliques in Social Networks: A New Distribution-Free Model}},
  booktitle =	{45th International Colloquium on Automata, Languages, and  Programming (ICALP 2018)},
  pages =	{55:1--55:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9059},
  URN =		{urn:nbn:de:0030-drops-90596},
  doi =		{10.4230/LIPIcs.ICALP.2018.55},
  annote =	{Keywords: Graph algorithms, social networks, fixed-parameter tractability}
}

Keywords: Graph algorithms, social networks, fixed-parameter tractability
Collection: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Issue Date: 2018
Date of publication: 04.07.2018

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