New Community Estimation Method in Bipartite Networks Based on Quality of Filtering Coefficient

Community detection is an important task in network analysis, in which we aim to find a network partitioning that groups together vertices with similar community-level connectivity patterns. Bipartite networks are a common type of network in which there are two types of vertices, and only vertices of different types can be connected. While there are a range of powerful and flexible methods for dividing a bipartite network into a specified number of communities, it is an open question how to determine exactly how many communities one should use, and estimating the numbers of pure-type communities in a bipartite network has not been completed. In our paper, we propose a method named as biCNEQ (bipartite network communities number estimation based on quality of filtering coefficient), which ensures that communities are all pure type, for estimating the number of communities in a bipartite network. This paper makes the following contributions: (1) we show how a unipartite weighted network, which we call similarity network, can be projected from a bipartite network using a measure of correlation; (2) we reveal the relation between the similarity correlation and community's edges in the vertices of a unipartite network; (3) we design a measure of the filtering quality named QFC (quality of filtering coefficient) to filter the similarity network and construct a binary network, which we call approximation network; and (4) the number of communities in each type of unipartite networks is estimated using Riolo's method with the approximation network as input. Finally, the proposed biCNEQ is demonstrated by both synthetic bipartite networks and a real-world network, and the results show that it can determine the correct number of communities and perform better than two classical one-mode projection methods.