Computing maximal cliques in link streams

• We introduce delta-cliques, that generalize graph cliques to link streams/time-varying graphs.
• We provide a greedy algorithm to compute all delta-cliques of a link stream.
• Implementation available on http://www.github.com/JordanV/delta-cliques.

A link stream is a collection of triplets (t,u,v)(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 Δ, a Δ-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 Δ. 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 to a real-world contact trace.