What if CLIQUE were fast? Maximum Cliques in Information Networks and Strong Components in Temporal Networks

Exact maximum clique finders have progressed to the point where we can investigate cliques in million-node social and information networks, as well as find strongly connected components in temporal networks. We use one such finder to study a large collection of modern networks emanating from biological, social, and technological domains. We show inter-relationships between maximum cliques and several other common network properties, including network density, maximum core, and number of triangles. In temporal networks, we find that the largest temporal strong components have around 20-30% of the vertices of the entire network. These components represent groups of highly communicative individuals. In addition, we discuss and improve the performance and utility of the maximum clique finder itself.