Modelling and monitoring social network change based on exponential random graph models

This paper aims to detect anomalous changes in social network structure in real time and to offer early warnings by phase II monitoring social networks. First, the exponential random graph model is used to model social networks. Then, a test and online monitoring technique of the exponential random graph model is developed based on the split likelihood-ratio test after determining the model and its parameters for a specific data set. This proposed approach uses pseudo-maximum likelihood estimation and likelihood ratio to construct the test statistics, avoiding the several steps of discovering Monte Carlo Markov Chain maximum likelihood estimation through an iterative method. A bisection algorithm for the control limit is given. Simulations on three data sets Flobusiness, Kapferer and Faux.mesa.high are presented to study the performance of the procedure. Different change points and shift sizes are compared to see how they affect the average run length. A real application example on the MIT reality mining social proximity network is used to illustrate the proposed modelling and online monitoring methods.