Monitoring the structure of social networks based on exponential random graph model

Abstract

Exponential random graph models (ERGM) are known as one of the most flexible models for profile monitoring of the complex structure of dynamic social networks, especially for networks with a large number of nodes. Usually, only one realization of a network is available instead of a random sample and the correlations between nodes increase the computational cost. Parametrizing via ERGM, the parameters of the model corresponding to the features of the network (namely, edges, $k$-star, and triangles) are then monitored using Hotelling’s $T^2$ and likelihood ratio test control charts in Phase I for two general scenarios in both the directed and undirected edges cases. The results show that the presented control charts efficiently characterize the profile consisting of a network at each sampling time. The power of each method at a constant nominal Type I error probability is numerically reported for different shifts in the parameters. The results are also employed in the analysis of Gnutella Internet Peer-to-Peer Networks.

Keywords:

• Change-point
• control chart
• exponential random graph model
• social network
• statistical process monitoring

Subject classification codes:

• 91D30
• 62H12
• 62H15