A spectral method of modularity for community detection in bipartite networks

¹ Business School, University of Shanghai for Science and Technology - Shanghai 200093, China
² College of Science, Guilin University of Aerospace Technology - Guilin, Guangxi 541004, China

^(a) gu_changgui@163.com (corresponding author)

Received: 27 November 2021
Accepted: 14 February 2022

Abstract

Community detection in bipartite networks is a popular topic. Two widely used methods to capture community structures in bipartite networks are the method of modularity and the method of graph partitioning. Our analytical results show that the modularity maximization problem can be reformulated as a spectral problem after relaxing the discreteness constraints. This means that the method of modularity and the method of graph partitioning are essentially equivalent. As an application, a spectral algorithm of modularity is devised for identifying community structures in bipartite networks. Experimental results on synthetic networks and real-world networks indicate that our algorithm performs better than those algorithms of modularity local maximization, such as BRIM (bipartite recursively induced moduls) and bLP (bipartite label propagation). Therefore, our results shed light on the methods of community detection in bipartite networks.