Clique-based Method for Social Network Clustering

In this paper, we develop some clique-based methods for social network clustering. The quality of clustering result is measured by a novel cliquebased index, which is innovated from the modularity index proposed in [12]. We design an effective algorithm based on recursive bipartition in order to maximize the objective function of the proposed index. Noting the optimization of the objective function is NP-hard when the network size or the parameter space is large, we relax the problem via an implicitly restarted Lanczos method from numerical algebra. One of the contributions of our method is that the proposed index of each community in the clustering result is higher than a predefined threshold, p, which is completely controlled by users. However, when the threshold is unknown or not given, we implement a tree-based strategy and propose a localized clustering algorithm which considers a localized threshold for each subnetwork to maximize the overall clique score of the ultimate clustering result. Finally, we exploit simulation experiments based on the stochastic block model to demonstrate the accuracy and efficiency of our algorithms, numerically and graphically.