A benefit function for community detection based on edge and path of length two

Abstract

In the field of community detection in complex networks, the most commonly used approach to this problem is the maximization of the benefit function known as “modularity”. In this study, it is found that the path of length two have the similar property as the edge, which is denser within communities and sparser between different communities. In order to take both edge and path of length two into consideration simultaneously, a self-loop is added to each node of the network and a novel benefit function has been defined. To divide the network into two communities, a second eigenvector method is proposed based on maximization of our new benefit function. Experimental results obtained by applying the method to karate club network and dolphin social network show the feasibility of our benefit function and the effectiveness of our algorithm.