Optimisation dans la d\'etection de communaut\'es recouvrantes et \'equilibre de Nash

TL;DR

This paper presents a novel algorithm for community detection in graphs that guarantees a Nash equilibrium by optimizing a potential function, improving upon heuristic methods for overlapping communities.

Contribution

Introduces an algorithm that modifies approximate solutions to reach a local optimum, ensuring a Nash equilibrium in community detection.

Findings

Algorithm guarantees a Nash equilibrium.

Effective detection of overlapping communities.

Experimental results demonstrate improved performance.

Abstract

Community detection in graphs has been the subject of many algorithms. Recent methods want to optimize a modularity function which shows a maximum of relationships within communities and found a minimum of inter-community relations. these algorithms are applied to unipartite, multipartite and directed graphs. However, given the NP-completeness of the problem, these algorithms are heuristics that do not guarantee an optimum. In this paper we introduce an algorithm which, based on an approximate solution obtained through a efficient detection algorithm, modifie it to achieve a local optimum based on a function. this reassignment function is a potential function and therefore the computed optimum is a Nash equilibrium. We supplement our method with an overlap function that allows to have simultaneously the two detection modes. Several experiments show the interest of our approach.