Clustering coefficient and community structure of bipartite networks

Many real-world networks display natural bipartite structure, where the basic cycle is a square. In this paper, with the similar consideration of standard clustering coefficient in binary networks, a definition of the clustering coefficient for bipartite networks based on the fraction of squares is proposed. In order to detect community structures in bipartite networks, two different edge clustering coefficients LC4 and LC3 of bipartite networks are defined, which are based on squares and triples respectively. With the algorithm of cutting the edge with the least clustering coefficient, communities in artificial and real world networks are identified. The results reveal that investigating bipartite networks based on the original structure can show the detailed properties that is helpful to get deep understanding about the networks.