Extending the definition of modularity to directed graphs with overlapping communities

Understand

Complex networks topologies present interesting and surprising properties, such as community structures, which can be exploited to optimize communication, to find new efficient and context-aware routing algorithms or simply to understand the dynamics and meaning of relationships among nodes.

• Complex networks are gaining more and more importance as a reference model and are a powerful interpretation tool for many different kinds of natural, biological and social networks, where directed relationships and contextual belonging of nodes to many different communities is a matter of fact.
• This paper starts from the definition of modularity function, given by M.
• Newman to evaluate the goodness of network community decompositions, and extends it to the more general case of directed graphs with overlapping community structures.