Finding all maximal connected S-cliques in social networks

Cliques are commonly used for social network analysis tasks, as they are a good representation of close-knit groups of people. For this reason (as well as for others), the problem of enumerating, i.e., finding, all maximal cliques in a graph has received extensive treatment. However, considering only complete subgraphs is too restrictive in many real-life scenarios where “almost cliques” may be even more useful. Hence, the notion of an s-clique, a clique relaxation that allows every node to be at distance at most s from every other node, has been introduced. Connected s-cliques add the natural requirement of connectivity to the notion of an s-clique. This paper presents efficient algorithms for finding all maximal connected s-cliques in a graph. We present a provably efficient algorithm, which runs in polynomial delay. In addition, we present several variants of the well-known Bron-Kerbosch algorithm for maximal clique generation. Extensive experimentation over both real and synthetic datasets shows the efficiency of our algorithms, and their scalability with respect to graph size, density, and choice of s.