Listing All Maximal $k$-Plexes in Temporal Graphs
Matthias Bentert, Anne-Sophie Himmel, Hendrik Molter, Marco Morik,, Rolf Niedermeier, Ren\'e Saitenmacher

TL;DR
This paper introduces an improved recursive algorithm to enumerate all maximal temporal $k$-plexes in evolving networks, extending previous work on $ ext{Δ}$-cliques, with demonstrated practical efficiency on real-world social network data.
Contribution
It extends the Bron-Kerbosch algorithm to efficiently enumerate maximal temporal $k$-plexes, generalizing $ ext{Δ}$-cliques, and provides experimental validation on real social networks.
Findings
Algorithm is significantly faster for $ ext{Δ}$-1-plexes compared to previous methods.
Practical feasibility demonstrated on real-world social network data.
Extension to $k$-plexes broadens community detection in temporal graphs.
Abstract
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 time-stamped 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 -cliques as a natural temporal version of cliques. Himmel et al. [SNAM 2017] showed how to adapt the well-known Bron-Kerbosch algorithm to enumerate -cliques. We continue this work and improve and extend the algorithm of Himmel et al. to enumerate temporal -plexes (notably, cliques are the special case ). We define a…
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