  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.
