Computing maximal cliques in link streams

Abstract

A link stream is a collection of triplets $(t, u, v)$ indicating that an interaction occurred between u and v at time t. We generalize the classical notion of cliques in graphs to such link streams: for a given $\Delta$, a $\Delta$-clique is a set of nodes and a time interval such that all pairs of nodes in this set interact at least once during each sub-interval of duration $\Delta$. We propose an algorithm to enumerate all maximal (in terms of nodes or time interval) cliques of a link stream, and illustrate its practical relevance on a real-world contact trace