Monitoring network data by considering the correlation of network feature statistics

Network monitoring has wide applications in computer and social network surveillance， pathological diagnosis in neuroscience and bioscience among others. Motivated by a real example of brain networks, we focus our interests on monitoring networks by considering correlations of feature statistics. Structural statistics of numbers of edges, stars and triangles, are adopted to summarize the main features of a network-density, degree variability, and transitivity. A multivariate chart is proposed to monitor the multiple statistics simultaneously, which has not been paid much attention to in previous studies. A simulation study is conducted to compare the performances of the multivariate chart and individual charts for the structural statistics as well as a model-based approach as a benchmark. The results show that the multivariate chart for the structural statistics perform well in most scenarios. In particular, it is more advantageous in timely detecting large shifts of connection propensity and degree variability locally and globally. A real case of monitoring Enron email networks is analyzed as an illustration.