Dynamic Exponential Random Graph Models with the Fused Lasso Penalty

This paper examines temporal variations in neighborhood connectivity structures across dynamic networks. We focus on ensembles of networks that exhibit sudden structural changes at certain time points but remain stable or undergo minimal changes in between. Many real-world networks, such as international trade networks and political co-voting networks, display this behavior. We introduce a novel fused lasso exponential random graph model (FL-ERGM) to characterize the dynamic evolution of network topology and to capture similar connectivity patterns across consecutive time points. Moreover, the model can detect abrupt structural changes at specific time points. To address the intractability of the ERGM likelihood, we adopt a pseudo-likelihood approximation. We optimize the resulting penalized pseudo-likelihood function using the alternating direction method of multipliers (ADMM), and we prove that the solution obtained by ADMM is equivalent to the optimal solution of the original objective function. Monte Carlo simulations demonstrate that FL-ERGM outperforms existing methods. Applications to international trade and political co-voting networks reveal interpretable and contextually relevant patterns of structural change.