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.
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