Identification of community structure in networks with convex optimization

Roland Hildebrand (1)

1 CASYS - Calculs Algébriques et Systèmes Dynamiques

We reformulate the problem of modularity maximization over the set of partitions of a network as a conic optimization problem over the completely positive cone, converting it from a combinatorial optimization problem to a convex continuous one. A semidefinite relaxation of this conic program then allows to compute upper bounds on the maximum modularity of the network. Based on the solution of the corresponding semidefinite program, we design a randomized algorithm generating partitions of the network with suboptimal modularities. We apply this algorithm to several benchmark networks, demonstrating that it is competitive in accuracy with the best algorithms previously known. We use our method to provide the first proof of optimality of a partition for a real-world network.

Mots clés: community structure; modularity

Domaines: Analyse de données, Statistiques et Probabilités [physics.data-an]; Mécanique statistique [cond-mat.stat-mech]; Physique et Société [physics.soc-ph]

Roland Hildebrand. Identification of community structure in networks with convex optimization. 2008. ⟨hal-00286959v2⟩