Listing all maximal k-plexes in temporal graphs

Matthias Bentert, Anne Sophie Himmel, Hendrik Molter, Marco Morik, Rolf Niedermeier, René Saitenmacher

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Many real-world 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 (which represent people in the case of social networks) are represented by timestamped edges. One of the most fundamental problems in (social) network analysis is community detection, and 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 BronKerbosch algorithm to enumerate Δ-cliques. We continue this work and improve and extend the algorithm of Himmel et al. to enumerate temporal k-plexes (notably, cliques are the special case k = 1). We define a Δ-k-plex as a set of vertices and a time interval, where during this time interval each vertex has in each consecutive Δ + 1 timesteps at least one edge to all but at most k − 1 vertices in the chosen set of vertices. We develop a recursive algorithm for enumerating all maximal Δ-k-plexes and perform experiments on real-world social networks that demonstrate the practical feasibility of our approach. In particular, for the special case of Δ-1-plexes (i.e., Δ-cliques), we observe that our algorithm is on average significantly faster than the previous algorithms by Himmel et al. [SNAM 2017] and Viard et al. [IPL 2018] for enumerating Δ-cliques.

Original languageEnglish
Article number113
JournalJournal of Experimental Algorithmics
Issue number1
StatePublished - 1 Sep 2019
Externally publishedYes


  • Community detection
  • Data science
  • Degeneracy
  • Experimental analysis
  • Link streams
  • Social network analysis
  • Temporal cliques
  • Time-varying networks

ASJC Scopus subject areas

  • Theoretical Computer Science


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