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

Mahboubeh Mohebbi, Amirhossein Amiri and Ali Reza Taheriyoun

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 10, 3742-3757

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 T2 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.

Date: 2024
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DOI: 10.1080/03610926.2022.2163366

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