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Temporal exponential random graph models (TERGM) are powerful statisticalmodels that can be used to infer the temporal pattern of edge formation andelimination in complex networks (e.g., social networks). TERGMs can also beused in a generative capacity to predict longitudinal time series data in theseevolving graphs. However, parameter estimation within this framework fails tocapture many real-world properties of social networks, including: triadicrelationships, small world characteristics, and social learning theories whichcould be used to constrain the probabilistic estimation of dyadic covariates.Here, we propose triadic temporal exponential random graph models (TTERGM) tofill this void, which includes these hierarchical network relationships withinthe graph model. We represent social network learning theory as an additionalprobability distribution that optimizes Markov chains in the graph vectorspace. The new parameters are then approximated via Monte Carlo maximumlikelihood estimation. We show that our TTERGM model achieves improved fidelityand more accurate predictions compared to several benchmark methods on GitHubnetwork data.

Triadic Temporal Exponential Random Graph Models (TTERGM)