Source
Title
An Introduction to Exponential Random Graph (p*) Models for Social Networks
Author
Mark S. Handcock
Publication
Social Networks (via CMU)
URL
https://www.stat.cmu.edu/~handcock/ergm/ergm_intro.pdf
Language
en

Summary

Exponential Random Graph Models (ERGMs) treat network ties as interdependent — the probability of a graph depends on structural statistics (edge count, reciprocity, transitivity, star configurations) through an exponential family formulation. Unlike naive Bernoulli edges, ERGM acknowledges that tie formation is structurally constrained.

Handcock's introduction walks through the motivation (why independence fails), sufficient statistics, and estimation challenges including degeneracy.

Key Points

  • ERGM specifies P(Y) ∝ exp(θ · g(Y)) where g(Y) are network statistics
  • Common statistics: edges, mutual, geometrically weighted edgewise shared partners (GWESP)
  • Degeneracy — some specifications concentrate probability on near-empty or near-full graphs
  • MCMC-MLE estimation in practice via ergm package in R
  • Interpretation is about tie odds conditional on structure, not causal mechanisms
My Note

ERGM is my default for cross-sectional network snapshots. I pair it with SIENA when temporal data exists. When teaching, I emphasize that ERGM success depends heavily on model specification — choosing statistics that match substantive theory without overfitting.

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