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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.