Abstract
Modern-day social networks evolve over time, that is, new contacts appear and old contacts may disappear. They can be modeled as temporal graphs where interactions between vertices (people) are represented by time-stamped edges. One of the most fundamental problems in social network analysis is community detection and within community detection, one of the most basic primitives to model a community is a clique. Addressing the problem of finding communities in temporal networks, Viard et al. [TCS 2016] introduced Δ-cliques as a natural temporal version of cliques. Himmel et al. [SNAM 2017] showed how to adapt the well-known Bron-Kerbosch algorithm for listing static cliques to listing Δ-cliques. We continue this work and improve and extend this algorithm to list temporal k-plexes, a temporal version of k-plexes, which are one of many popular clique relaxations. We define a Δ- k-plex as a set of vertices with a lifetime, where during the lifetime each vertex has an edge to all but at most k-1 vertices at least once every Δ + 1 consecutive time steps. We develop an algorithm for listing all maximal Δ- k-plexes and perform experiments on real-world networks that demonstrate the practical feasibility of our approach. In particular, for the special case of listing Δ-1-plexes (Δ-cliques), we observe that our algorithm is significantly faster than the previous algorithm by Himmel et al.