Detecting the overlapping and hierarchical community structure in complex networks

TLDR

Many networks in nature, society, and technology exhibit mesoscopic organization where tightly connected groups (communities or modules) are weakly linked, often hierarchically nested and overlapping, making community detection a key challenge in complex networks. The authors introduce the first algorithm that simultaneously detects overlapping communities and hierarchical organization. The algorithm optimizes a fitness function locally, identifies community structure from peaks in the fitness histogram, and allows resolution tuning to explore different hierarchical levels. Experiments on real and synthetic networks demonstrate excellent performance.

Abstract

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. 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 is based on the local optimization of a fitness function. Community structure is revealed by peaks in the fitness histogram. The resolution can be tuned by a parameter enabling different hierarchical levels of organization to be investigated. Tests on real and artificial networks give excellent results.