Detecting the overlapping and hierarchical community structure of complex networks
S. Fortunato (Complex Networks Lagrange Laboratory, Institute for Scientific Interchange, Turin, Italy), A. Lancichinetti (Complex Networks Lagrange Laboratory, Institute for Scientific Interchange, Turin, Italy) and J. Kertesz (Department of Theoretical Physics, Budapest University of Technology and Economics, Budapest, Hungary)
Many networks in nature, society and technology display a mesoscopic level of organization, with groups of nodes forming tighly connected units ("communities"), that are only weakly linked to each other. Most methods of community detection usually do not consider that a network may have hierarchical levels of organization, with communities embedded within other communities, and that nodes can be shared between different communities.
Here we present the first algorithm that finds both overlapping communities and hierarchical structure.
Tests on real and artificial networks give excellent results. The method is very fast, and allows to analyse systems with millions of nodes.