Soft Overlapping Community Detection in Large-Scale Networks via Fast Fuzzy Modularity Maximization

Soft overlapping clustering is one of the notable problems of community detection. Extensive research has been conducted to develop efficient methods for nonoverlapping and crisp-overlapping community detection in large-scale networks. In this article, fast fuzzy modularity maximization (FFMM) for soft overlapping community detection is proposed. FFMM exploits novel iterative equations to calculate the modularity gain associated with changing the fuzzy membership values of network vertices. The simplicity of the proposed scheme enables efficient modifications, reducing computational complexity to a linear function of the network size, and the number of communities. Moreover, to further reduce the complexity of FFMM for very large networks, multicycle FFMM (McFFMM) is proposed. The proposed McFFMM reduces complexity by breaking networks into multiple subnetworks and applying FFMM to detect their communities. Performance of the proposed techniques is demonstrated with real-world data and the Lancichinetti-Fortunato-Radicchi benchmark networks. Moreover, the performance of the proposed techniques is evaluated versus some state-of-the-art soft overlapping community detection approaches. Results show that the McFFMM produces a remarkable performance in terms of overlapping modularity with fuzzy memberships, computational time, number of detected overlapping nodes, and overlapping normalized mutual information.