A Declarative Framework for Maximal k-plex Enumeration Problems
Résumé
It is widely accepted that an ideal community in networks is the one
whose structure is closest to a (maximal) clique. However, in most
real-world graphs the clique model is too restrictive, as it requires
complete pairwise interactions. More relaxed 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, by involving irrelevant subgraphs, are far
from designing meaningful communities in real-world networks. In
this paper, we first introduce a novel variant of k-plex model, called
cohesive k-plex, which is more appropriate for modeling closely-
interacting communities. Then, we reduce the problem of enumerat-
ing 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 decomposition technique
that is particularly suitable for deriving smaller and independent
sub-problems easy to resolve. Lastly, our extensive experiments
on various real-world graphs demonstrate the efficiency of the
proposed approach w.r.t state-of-the-art algorithms.