Modularity for Bipartite Networks
Several real-world data are represented as bipartite networks composed of two types of vertices, such as paper–author networks and event–attendee networks. Discovering communities from such bipartite networks is important for finding similar items and for understanding overall network structures. In order to evaluate the quality of divisions of normal (unipartite) networks, Newman’s modularity is widely used. Recently, modularities for bipartite networks are proposed by Guimera and Barber. These bipartite modularities are, however, not sufficient for evaluating the degree of correspondence between communities of different vertex types, which is often important for understanding the characteristics of the communities. For example, close-knit paper communities and author communities indicate that their research topics are relatively focused rather than loose-knit communities. This chapter proposes a new bipartite modularity for evaluating community extraction from bipartite networks. Experimental results show that our new bipartite modularity is appropriate for discovering close-knit communities, and it is also useful for characterizing the communities.
The author would like to thank Mr. Makoto Okamoto, Prof. Kikuo Maekawa (The National Institute for Japanese Language), and Prof. Sadaoki Furui (Tokyo Institute of Technology) for allowing us to use the data of Yahoo! Chiebukuro.
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