A Novel Similarity-based Modularity Func- tion for Graph Partitioning

Graph partitioning, or network clustering, is an essential research problem in many areas. Current approaches, however, have difficulty splitting two clusters that are densely connected by one or more "hub" vertices. Further, traditional methods are less able to deal with very confused structures. In this paper we propose a novel similarity-based definition of the quality of a parti- tioning of a graph. Through theoretical analysis and experimental results we demonstrate that the proposed definition largely overcomes the "hub" problem and outperforms existing approaches on complicated graphs. In addition, we show that this definition can be used with fast agglomerative algorithms to find communities in very large networks.