A fast and complete enumeration of pseudo-cliques for large graphs

Abstract

This paper discusses a complete and efficient algorithm for enumerating densely-connected k-Plexes. A k-Plex is a kind of pseudoclique which imposes a Disconnection Upper Bound (DUB) by the parameter k for each constituent vertex. However, since the parameter is usually fixed not depending on sizes of our targeted pseudo-cliques, we often have k-Plexes not densely-connected. In order to overcome this drawback, we introduce another constraint using a parameter j designating Connection Lower Bound (CLB). Based on CLB, we can additionally enjoy a monotonic j-core operation and design an efficient depth-first algorithm which can exclude hopeless vertex sets which cannot be extended to their supersets satisfying both DUB and CLB. Our experimental results show it can work well as a useful tool for detecting densely-connected pseudo cliques in large networks including one with over 800, 000 vertices.