2k: Scalable community detection in massive networks via small-diameter k-plexes

This paper studies k-plexes, a well known pseudo-clique model for network communities. In a k-plex, each node can miss at most k - 1 links. Our goal is to detect large communities in today's real-world graphs which can have hundreds of millions of edges. While many have tried, this task has been elusive so far due to its computationally challenging nature: k-plexes and other pseudo-cliques are harder to find and more numerous than cliques, a well known hard problem. We present d2k, which is the first algorithm able to find large k-plexes of very large graphs in just a few minutes. The good performance of our algorithm follows from a combination of graph-theoretical concepts, careful algorithm engineering and a high-performance implementation. In particular, we exploit the low degeneracy of real-world graphs, and the fact that large enough k-plexes have diameter 2. We validate a sequential and a parallel/distributed implementation of d2k on real graphs with up to half a billion edges.