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 nonadjacent vertices with $c$ common neighbors. Numerical experiments show that well-studied social networks with thousands of vertices tend to be weakly $c$-closed for modest values of $c$.

Keywords

  1. graph algorithms
  2. social networks
  3. fixed-parameter tractability

MSC codes

  1. 68Q27
  2. 68W40
  3. 68R10

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Information & Authors

Information

Published In

cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 448 - 464
ISSN (online): 1095-7111

History

Submitted: 29 August 2018
Accepted: 6 January 2020
Published online: 27 April 2020

Keywords

  1. graph algorithms
  2. social networks
  3. fixed-parameter tractability

MSC codes

  1. 68Q27
  2. 68W40
  3. 68R10

Authors

Affiliations

Funding Information

Packard Fellowship
Alfred P. Sloan Foundation https://doi.org/10.13039/100000879
National Science Foundation https://doi.org/10.13039/100000001 : DMS-1352121
National Science Foundation https://doi.org/10.13039/100000001 : CCF-1524062
National Science Foundation https://doi.org/10.13039/100000001 : CCF-1319080, CCF-1740850
National Science Foundation https://doi.org/10.13039/100000001

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