Modularity for heterogeneous networks

Online social media such as delicious and digg are represented as tripartite networks whose vertices are users, tags, and resources. Detecting communities from such tripartite networks is practically important. Modularity is often used as the criteria for evaluating the goodness of network divisions into communities. Although Newman-Girvan modularity is popular for unipartite networks, it is not suitable for n-partite networks. For bipartite networks, Barber, Guimera, Murata and Suzuki define bipartite modularities. For tripartite networks, Neubauer defines tripartite modularity which extends Murata's bipartite modularity. However, Neubauer's tripartite modularity still uses projections and it will lose information that original tripartite networks have. This paper proposes new tripartite modularity for tripartite networks that do not use projections. Experimental results show that better community structures can be detected by optimizing our tripartite modularity.

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