Enumerating maximal clique sets with pseudo-clique constraint

Abstract

It is an important task in Data Mining and Social Network Analysis to detect dense subgraphs, namely pseudo-cliques in networks. Given a positive integer k designating an upper bound of the number of disconnections, some algorithms to enumerate k-plexes as pseudo-cliques have been proposed based on the anti-monotonicity property similar to the case of cliques. Those algorithms are however effective only for small k, since every vertex set with its size less than k +1 is trivially a k-plex. Moreover, there still exist non-dense k-plexes with their sizes exceeding k. For these reasons, it has been a hard task to design an efficient k-plex enumerator for non-small k. This paper aims at developing a fast enumerator for finding densely connected k-plexes for non-small k, avoiding both of the small k-plexes and non-dense medium k plexes. For this purpose, we construct a clique-graph from the original input graph and consider meta-cliques of overlapping cliques satisfying several constraints about k-plexness and overlappingness using bond measure for set-theoretic correlation. We also show its usefulness by exhaustive experiments about the number of solution k-plexes, computational costs and even the quality of output k-plexes.