Detecting communities in complex networks using triangles and modularity density

Abstract

The community structure is an important property of complex networks. Community detection of complex networks can be used to help reveal the relationship between topology and functionality. Modularity density QD, as a community quality function, has been widely used for detection of community structure in networks. Here, we develop a novel modularity density based on triangular motifs, and also prove its equivalence with the spectral clustering and non-negative matrix factorization. In addition, we develop a community detection method that incorporates the edge and triangular motif information, and apply the proposed method to several classical complex networks. Experiments show that the proposed method outperforms the standard modularity density QD.