A New Tripartite Modularity for Detecting Communities

Abstract

Many users are attracted by online social media such as Delicious and Digg, and they put tags on online resources. Relations among users, tags, and resources are represented as a tripartite network composed of three types of vertices. Detecting communities (densely connected subnetworks) from such tripartite networks is important for finding similar users, tags, and resources. For unipartite networks, several attempts have been made for detecting communities, and one of the popular approaches is to optimize modularity, a measurement for evaluating the goodness of network divisions. Modularity for bipartite networks is proposed by Barber, Guimera, Murata and Suzuki. However, as far as the author knows, there is few attempt for defining modularity for tripartite networks. This paper defines a new tripartite modularity which indicates the correspondence between communities of three vertex types. By optimizing the value of our tripartite modularity, better community structures can be detected from synthetic tripartite networks.