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

Abstract

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.

Keywords:

• Exponentially random graph model
• online monitoring
• social network
• split likelihood ratio test
• statistical process control

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors are grateful to the editor, the associate editor and three anonymous referees for their comments that have greatly improved this paper. This research was supported by National Key R &D Program of China [grant 2022ZD0114801], National Natural Science Foundation of China [grants 12071233, 12075162 and 11971247], Natural Science Foundation of Fujian Province, China [grant 2022J02050] VC&VR Key Lab of Sichuan Province.