Statistical mechanics of networks: Estimation and uncertainty

B. A. Desmarais, S. J. Cranmer

Research output: Contribution to journalArticlepeer-review

83 Scopus citations


Exponential random graph models (ERGMs) are powerful tools for formulating theoretical models of network generation or learning the properties of empirical networks. They can be used to construct models that exactly reproduce network properties of interest. However, tuning these models correctly requires computationally intractable maximization of the probability of a network of interestmaximum likelihood estimation (MLE). We discuss methods of approximate MLE and show that, though promising, simulation based methods pose difficulties in application because it is not known how much simulation is required. An alternative to simulation methods, maximum pseudolikelihood estimation (MPLE), is deterministic and has known asymptotic properties, but standard methods of assessing uncertainty with MPLE perform poorly. We introduce a resampling method that greatly outperforms the standard approach to characterizing uncertainty with MPLE. We also introduce ERGMs for dynamic networkstemporal ERGM (TERGM). In an application to modeling cosponsorship networks in the United States Senate, we show how recently proposed methods for dynamic network modeling can be integrated into the TERGM framework, and how our resampling method can be used to characterize uncertainty about network dynamics.

Original languageEnglish (US)
Pages (from-to)1865-1876
Number of pages12
JournalPhysica A: Statistical Mechanics and its Applications
Issue number4
StatePublished - Feb 15 2012

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics


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