D-HOCS: an algorithm for discovering the hierarchical overlapping community structure of a social network

Social networks often demonstrate a hierarchical organization, with communities embedded within other communities; moreover, nodes can be shared between different communities, i.e. communities in social networks may be overlapping. In this paper, we define a hierarchical overlapping community structure to present overlapping communities of a social network at different levels of granularity. Discovering the hierarchical overlapping community structure of a social network can provide us a deeper understanding of the complex nature of social networks. We propose an algorithm, called D-HOCS, to derive the hierarchical overlapping community structure of social networks. Firstly, D-HOCS generates a probability transition matrix by applying random walk to a social network, and then trains a Gaussian Mixture Model using the matrix. Further D-HOCS derives overlapping communities by analyzing mean vectors of the Gaussian mixture model. Varying the number of components, D-HOCS repeatedly trains the Gaussian mixture model, detecting the overlapping communities at different levels of granularity. Organizing the overlapping communities into a hierarchy, D-HOCS can finally obtain the hierarchical overlapping community structure of the social network. The experiments conducted on synthetic and real dataset demonstrate the feasibility and applicability of the proposed algorithm. We further employ D-HOCS to explore Enron e-mail corpus, and obtain several interesting insights. For example, we find out a coordinator who coordinated many sections of the Enron Corporation to complete an important task during first half of 2001. We also identify a community that corresponds to a real organization in Enron Corporation.