A Spectral Clustering Approach Based on Modularity Maximization for Community Detection Problem

Modularity is widely-used objective function to detect communities and there are lots of algorithms based on modularity maximization. The leading eigenvector method is one of them where modularity is maximized by choosing the first eigenvector as partition result. To analyze in depth the information provided by other eigenvectors, modularity maximization could be transformed to vector partitioning problem. This paper proposes a method to find non-overlapping vertex vector sets so as to maximize the quadratic sum of norms of community vectors. We observe spatial distribution of the vertex vectors of networks and then discover two phenomenons. First, the vertex vectors belong to different communities are separated by an angle. Second, the node with a larger degree would correspond to a vertex vector with a larger norm. Based on these two phenomena, we design a heuristic community detection algorithm. When a network with weaker community structure, the over-partition problem is considered. The experiment results show that the proposed solution provides higher accuracy than other solutions.