On weakly optimal partitions in modular networks

José Ignacio Alvarez-Hamelin (1, 2) , Beiró Mariano Gastón (1) , Jorge Rodolfo Busch (1)

1 FIUBA - Facultad de Ingeniería [Buenos Aires]
2 INTECIN - Instituto de Tecnologías y Ciencias de la Ingeniería "Hilario Fernández Long" [Buenos Aires]

Modularity was introduced as a measure of goodness for the community structure induced by a partition of the set of vertices in a graph. Then, it also became an objective function used to find good partitions, with high success. Nevertheless, some works have shown a scaling limit and certain instabilities when finding communities with this criterion. Modularity has been studied proposing several formalisms, as hamiltonians in a Potts model or laplacians in spectral partitioning. In this paper we present a new probabilistic formalism to analyze modularity, and from it we derive an algorithm based on weakly optimal partitions. This algorithm obtains good quality partitions and also scales to large graphs.

Mots clés: modularity; community structure; algorithms; complex systems

Domaines: Réseaux et télécommunications [cs.NI]; Mécanique statistique [cond-mat.stat-mech]

José Ignacio Alvarez-Hamelin, Beiró Mariano Gastón, Jorge Rodolfo Busch. On weakly optimal partitions in modular networks. 2010. ⟨hal-00510596⟩