An introduction to exponential random graph (p*) models for social networks

Garry Robins*, Pip Pattison, Yuval Kalish, Dean Lusher

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This article provides an introductory summary to the formulation and application of exponential random graph models for social networks. The possible ties among nodes of a network are regarded as random variables, and assumptions about dependencies among these random tie variables determine the general form of the exponential random graph model for the network. Examples of different dependence assumptions and their associated models are given, including Bernoulli, dyad-independent and Markov random graph models. The incorporation of actor attributes in social selection models is also reviewed. Newer, more complex dependence assumptions are briefly outlined. Estimation procedures are discussed, including new methods for Monte Carlo maximum likelihood estimation. We foreshadow the discussion taken up in other papers in this special edition: that the homogeneous Markov random graph models of Frank and Strauss [Frank, O., Strauss, D., 1986. Markov graphs. Journal of the American Statistical Association 81, 832-842] are not appropriate for many observed networks, whereas the new model specifications of Snijders et al. [Snijders, T.A.B., Pattison, P., Robins, G.L., Handock, M. New specifications for exponential random graph models. Sociological Methodology, in press] offer substantial improvement.

Original languageEnglish
Pages (from-to)173-191
Number of pages19
JournalSocial Networks
Issue number2
StatePublished - May 2007
Externally publishedYes


  • Exponential random graph models
  • Statistical models for social networks
  • p models


Dive into the research topics of 'An introduction to exponential random graph (p*) models for social networks'. Together they form a unique fingerprint.

Cite this