## 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.

Original language | English (US) |
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Pages (from-to) | 448-464 |

Number of pages | 17 |

Journal | SIAM Journal on Computing |

Volume | 49 |

Issue number | 2 |

DOIs | |

State | Published - 2020 |

## All Science Journal Classification (ASJC) codes

- General Computer Science
- General Mathematics

## Keywords

- Fixed-parameter tractability
- Graph algorithms
- Social networks