Continuous Time Graph Processes with Known ERGM Equilibria: Contextual Review, Extensions, and Synthesis

Area of Science:

• Network Science
• Computational Social Science
• Mathematical Sociology

Background:

• Continuous-time graph processes offer high temporal resolution for modeling dynamic networks.
• They naturally represent structural changes as they occur, unlike discrete-time models.
• Stochastic actor-oriented models (SAOMs) are a prominent example widely used in social sciences.

Purpose of the Study:

• To review conditions for the convergence of continuous-time graph processes to known distributions.
• To present examples of existing and novel continuous-time graph processes with known convergence properties.
• To contextualize these processes within broader network dynamics research.

Main Methods:

• Review of theoretical conditions for convergence in continuous-time graph processes.
• Analysis of existing models, including subfamilies of stochastic actor-oriented models.
• Examination of continuum extensions of temporal and separable temporal exponential family random graph models.

Main Results:

• Identified conditions under which continuous-time graph processes converge to specific graph distributions.
• Provided examples of such processes, encompassing established and new frameworks.
• Highlighted the applicability of these models in social network analysis and beyond.

Conclusions:

• Continuous-time graph processes are valuable for understanding social network dynamics with high fidelity.
• The convergence properties of these models are crucial for theoretical development and empirical application.
• Further research into continuous-time network models promises advancements in network science.