Fast enumeration of large k-Plexes

k-plexes are a formal yet flexible way of defining communities in networks. They generalize the notion of cliques and are more appropriate in most real cases: while a node of a clique C is connected to all other nodes of C, a node of a k-plex may miss up to k connections. Unfortunately computing all maximal k-plexes is a gruesome task and state-of-the-art algorithms can only process small-size networks. In this paper we propose a new approach for enumerating large k-plexes in networks that speeds up the search by several orders of magnitude, leveraging on (i) methods for strongly reducing the search space and (ii) efficient techniques for the computation of maximal cliques. Several experiments show that our strategy is effective and is able to increase the size of the networks for which the computation of large k-plexes is feasible from a few hundred to several hundred thousand nodes.