Maximal Labelled-Clique and Click-Biclique Problems for Networked Community Detection

Discovering "closely related entities" in any network, a.k.a. communities, is a key goal for various network analytic applications. In particular, cliques and bicliques are two community structures that have influenced several tools and techniques in Big Data and social networking. A clique is a complete subgraph of an undirected graph and similarly, a biclique is a complete bipartite subgraph. A maximal clique (or biclique) is a clique that is not subset of any other clique (or biclique). Algorithms to list all maximal cliques in general graphs or bicliques in bipartite graphs have been previously studied. In this paper, we enhance these solutions explaining how a novel structure, that we call clique-biclique can be used to unravel richer communities with respect to different problems in a wide variety of networks. We then give two algorithms for efficiently listing maximal labelled-cliques and maximal clique-bicliques. The first algorithm is an extension of the maximal clique enumeration and the second cleverly combines enumeration of maximal cliques and maximal bicliques. We conduct an experimental analysis over different synthetic and real datasets to evaluate performance of the algorithms, and we found that even richer communities compared to cliques and bicliques can be efficiently found in most networks of interest.