An Efficient Control Chart for Monitoring Unweighted Networks With Overlapping Communities

In recent years, detecting anomalies in networks has attracted much attention in the literature. Researchers have developed various statistical process control (SPC) techniques to monitor the communication level within the networks. It is quite common to see the nodes belonging to some densely connected communities or subgroups and the nodes within a community communicate with each other more frequently than with nodes from other communities. However, we can find scarce SPC techniques that consider the multiple community labels and heterogeneity of nodes simultaneously. It is necessary to overcome this drawback to improve the change detection efficiency. This article establishes a new mixed-membership stochastic block model to characterize the multiple community labels and heterogeneity of nodes simultaneously. Then a new control chart is developed based on generalized likelihood ratio test (GLRT). The proposed control chart can be easily implemented in practice and avoids constant parameter estimation in Phase II monitoring. Numerous simulation studies and a real example show the advantages of proposed chart over existing ones.