Journal of Statistical Physics

, Volume 165, Issue 4, pp 740–754 | Cite as

Auxiliary Parameter MCMC for Exponential Random Graph Models

  • Maksym ByshkinEmail author
  • Alex Stivala
  • Antonietta Mira
  • Rolf Krause
  • Garry Robins
  • Alessandro Lomi


Exponential random graph models (ERGMs) are a well-established family of statistical models for analyzing social networks. Computational complexity has so far limited the appeal of ERGMs for the analysis of large social networks. Efficient computational methods are highly desirable in order to extend the empirical scope of ERGMs. In this paper we report results of a research project on the development of snowball sampling methods for ERGMs. We propose an auxiliary parameter Markov chain Monte Carlo (MCMC) algorithm for sampling from the relevant probability distributions. The method is designed to decrease the number of allowed network states without worsening the mixing of the Markov chains, and suggests a new approach for the developments of MCMC samplers for ERGMs. We demonstrate the method on both simulated and actual (empirical) network data and show that it reduces CPU time for parameter estimation by an order of magnitude compared to current MCMC methods.


ERGMs Parameter inference MCMC Social networks Supercomputing Snowball sampling 



This work was funded by PASC project “Snowball sampling and conditional estimation for exponential random graph models for large networks in high performance computing” and was supported by a grant from the Swiss National Supercomputing Centre (CSCS) under project ID c09. This research was also supported by a Victorian Life Sciences Computation Initiative (VLSCI) grant number VR0261 on its Peak Computing Facility at the University of Melbourne, an initiative of the Victorian Government, Australia.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Università della Svizzera italianaLuganoSwitzerland
  2. 2.University of MelbourneMelbourneAustralia

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