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Networks constitute powerful means of representing various types of complex systems, where nodes denote the system entities and edges express the interactions between the entities. An important topological property in complex networks is community structure, where the density of edges within subgraphs is much higher than across different subgraphs. Each of these subgraphs forms a community (or module). In literature, a metric called modularity is defined that measures the quality of a partition of nodes into different mutually exclusive communities. One means of deriving community structure is modularity maximisation. In this paper, a novel mathematical programming-based model, DiMod, is proposed that tackles the problem of maximising modularity for directed networks.

Community Structure Detection for Directed Networks through Modularity Optimisation