EWMA control charts using generalized centrality measures for social network monitoring

The monitoring and detection of network anomalies have become an interesting topic in social network analysis. One approach for detecting such anomalies is to apply conventional centrality measures, such as degree centrality, closeness centrality, and betweenness centrality, to control charts. Another approach involves the use of hybrid centrality measures, such as degree-degree, degree-closeness, and degree-betweenness, which are generated by combining traditional centrality measures and emphasize the importance of actors in the network. From another perspective, most studies on weighted networks have used centrality measures based on tie weights alone and have not accounted for the number of ties. In this paper, we propose exponentially weighted moving average (EWMA) charting procedures that use several types of centrality measures based on the number and weights of ties in undirected weighted networks. We then evaluate the anomaly-detection performance of these measures on weighted networks using EWMA charts. Simulation results indicate that degree and degree-degree centralities perform well for small changes, while betweenness and degree centralities perform well for large changes. In addition, centrality measures that consider both the number and weights of ties, with more importance given to the weights were determined to be better at detecting anomalies.