A Dynamic Process Interpretation of the Sparse ERGM Reference Model

Abstract

Exponential family random graph models (ERGMs) can be understood in terms of a set of structural biases that act on an underlying reference distribution. This distribution determines many aspects of the behavior and interpretation of the ERGM families incorporating it. One important innovation in this area has been the development of an ERGM reference model that produces realistic behavior when generalized to sparse networks of varying size. Here, we show that this model can be derived from a latent dynamic process in which tie formation takes place within small local settings between which individuals move. This derivation provides one possible micro-process interpretation of the sparse ERGM reference model, and sheds light on the conditions under which constant mean degree scaling can emerge.

References in corpus (1)

• Graph Evolution: Densification and Shrinking Diameters

Cited by in corpus (5)

• Exponential-Family Models of Random Graphs: Inference in Finite-, Super-, and Infinite Population Scenarios
• Parameter Estimation Procedures for Exponential-Family Random Graph Models on Count-Valued Networks: A Comparative Simulation Study
• Highly Scalable Maximum Likelihood and Conjugate Bayesian Inference for ERGMs on Graph Sets with Equivalent Vertices
• Continuous Time Graph Processes with Known ERGM Equilibria: Contextual Review, Extensions, and Synthesis
• Pseudo-likelihood-based $M$-estimation of random graphs with dependent edges and parameter vectors of increasing dimension