Detecting the overlapping and hierarchical community structure of complex networks

Many networks in nature, society and technology are characterized by a mesoscopic level of organization, with groups of nodes forming tightly connected units, called communities or modules, that are only weakly linked to each other. Uncovering this community structure is one of the most important problems in the field of complex networks and has countless applications in different disciplines like biology, computer and social sciences. Networks often show a hierarchical organization, with communities embedded within other communities; moreover, nodes can be shared between different communities. Here we present the first algorithm that finds both overlapping communities and the hierarchical structure. The method, based on the local optimization of a fitness function, is very fast and makes possible the analysis of systems with millions of nodes. Tests on real and artificial networks give excellent results.