A Declarative Framework for Maximal k-plex Enumeration Problems

Abstract

**Read paper on the following link:** https://ifaamas.org/Proceedings/aamas2022/pdfs/p660.pdf **Abstract:** It is widely accepted that an ideal community in networks is the onewhose structure is closest to a (maximal) clique. However, in most real-word graphs the clique model is too restrictive, as it requires complete pairwise interactions. More realistic and relaxed forms of cohesive subgraph models were then studied. A k-plex is one of the arguably most studied pseudo-clique model. A k-plex of size n is a subgraph where any vertex is adjacent to at least (n-k) vertices. Unfortunately, some maximal k-plexes are far from representing meaningful communities in complex networks. In this paper, we first introduce a novel variant of k-plex model, called cohesive k-plex, which is more appropriate for modeling real communities. Then, we reduce the problem of enumerating maximal cohesive k-plexes in a graph to those of enumerating the models of a formula in propositional logic. Afterwards, to make our approach more efficient, we provide a graph decomposition technique that is particularly suitable for deriving smaller and independent sub-problems easy to resolve. Finally, extensive experiments on real-world graphs confirm the efficiency and scalability of our proposed approach.