Anomaly detection in static networks using egonets

Network data has rapidly emerged as an important and active area of statistical methodology. In this paper we consider the problem of anomaly detection in networks. Given a large background network, we seek to detect whether there is a small anomalous subgraph present in the network, and if such a subgraph is present, which nodes constitute the subgraph. We propose an inferential tool based on egonets to answer this question. The proposed method is computationally efficient and naturally amenable to parallel computing, and easily extends to a wide variety of network models. We demonstrate through simulation studies that the egonet method works well under a wide variety of network models. We obtain some fascinating empirical results by applying the egonet method on several well-studied benchmark datasets.