Reformulation of a locally optimal heuristic for modularity maximization

Alberto Costa (1) , Sonia Cafieri (2) , Pierre Hansen (1, 3)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 MAIAA - ENAC - Laboratoire de Mathématiques Appliquées, Informatique et Automatique pour l'Aérien
3 HEC Montréal - HEC Montréal

A network, or graph, G = (V,E) consists of a set of vertices V = {1, . . . , n} and a set of edges E = {1, . . . ,m} connecting vertices. One of the most studied problems in the field of complex systems is to find communities, or clusters, in networks. A community consists of a subset S of the vertices of V where inner edges connecting pairs of vertices of S are more dense than cut edges connecting vertices of S to vertices of V \S. Many criteria have been proposed to evaluate partitions of V into communities.

Mots clés: binary decomposition; clustering; modularity maximization; reformulation

Domaines: Optimisation et contrôle [math.OC]

Alberto Costa, Sonia Cafieri, Pierre Hansen. Reformulation of a locally optimal heuristic for modularity maximization. ROADEF 2012, 13ème congrès annuel de la Société Française de Recherche Opérationnelle et d'Aide à la Décision, Apr 2012, Angers, France. ⟨hal-00934798⟩