Dense and Sparse Graph Partition

Julien Darlay (1) , Nadia Brauner (1) , Julien Moncel (1)

1 G-SCOP_ROSP - Recherche Opérationnelle pour les Systèmes de Production

In a graph, the density is the ratio between the number of edges and the number of vertices. This criterion may be used to find communities in a graph: groups of highly connected vertices. We propose an optimization problem based on this criterion, the idea is to find the vertex partition that maximizes the sum of the densities of each class. We prove that this problem is NP-hard by giving a reduction from graph-k-colorability. Additionally, we give a polynomial time algorithm for the special case of trees.

Mots clés: graph theory; community detection

Domaines: Recherche opérationnelle [math.OC]

Julien Darlay, Nadia Brauner, Julien Moncel. Dense and Sparse Graph Partition. Discrete Applied Mathematics, 2012, 160 (16 - 17), pp.2389 2396. ⟨hal-00454999⟩