Computing maximal cliques in link streams

• Published in: Theoretical computer science Vol. 609; no. Part 1; pp. 245 - 252
• Main Authors: Viard, Tiphaine, Latapy, Matthieu, Magnien, Clémence
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 04.01.2016; Elsevier
• Subjects: Algorithms; Cliques; Collection; Computation; Computer Science; Contact; Data Structures and Algorithms; Graphs; Intervals; Link streams; Links; Other; Streams; Temporal networks; Time-varying graphs; Link streams; Graphs; Algorithms; Cliques; Time-varying graphs; Temporal networks; algorithms; graphs; time-varying graphs; temporal networks; cliques; link streams
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2015.09.030

•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/TiphaineV/delta-cliques. 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 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.