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Exponential random graph model parameter estimation for very large directed networks

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  • Alex Stivala
  • Garry Robins
  • Alessandro Lomi

Abstract

Exponential random graph models (ERGMs) are widely used for modeling social networks observed at one point in time. However the computational difficulty of ERGM parameter estimation has limited the practical application of this class of models to relatively small networks, up to a few thousand nodes at most, with usually only a few hundred nodes or fewer. In the case of undirected networks, snowball sampling can be used to find ERGM parameter estimates of larger networks via network samples, and recently published improvements in ERGM network distribution sampling and ERGM estimation algorithms have allowed ERGM parameter estimates of undirected networks with over one hundred thousand nodes to be made. However the implementations of these algorithms to date have been limited in their scalability, and also restricted to undirected networks. Here we describe an implementation of the recently published Equilibrium Expectation (EE) algorithm for ERGM parameter estimation of large directed networks. We test it on some simulated networks, and demonstrate its application to an online social network with over 1.6 million nodes.

Suggested Citation

  • Alex Stivala & Garry Robins & Alessandro Lomi, 2020. "Exponential random graph model parameter estimation for very large directed networks," PLOS ONE, Public Library of Science, vol. 15(1), pages 1-21, January.
    • Handle: RePEc:plo:pone00:0227804
    DOI: 10.1371/journal.pone.0227804
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    References listed on IDEAS

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    1. Jones, Galin L. & Haran, Murali & Caffo, Brian S. & Neath, Ronald, 2006. "Fixed-Width Output Analysis for Markov Chain Monte Carlo," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1537-1547, December.
    2. Anna D. Broido & Aaron Clauset, 2019. "Scale-free networks are rare," Nature Communications, Nature, vol. 10(1), pages 1-10, December.
    3. Hunter, David R. & Handcock, Mark S. & Butts, Carter T. & Goodreau, Steven M. & Morris, Martina, 2008. "ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 24(i03).
    4. Morris, Martina & Handcock, Mark S. & Hunter, David R., 2008. "Specification of Exponential-Family Random Graph Models: Terms and Computational Aspects," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 24(i04).
    5. Gillespie, Colin S., 2015. "Fitting Heavy Tailed Distributions: The poweRlaw Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 64(i02).
    6. Hunter, David R. & Goodreau, Steven M. & Handcock, Mark S., 2008. "Goodness of Fit of Social Network Models," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 248-258, March.
    7. Babkin, Sergii & Stewart, Jonathan R. & Long, Xiaochen & Schweinberger, Michael, 2020. "Large-scale estimation of random graph models with local dependence," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    8. Krivitsky, Pavel N., 2017. "Using contrastive divergence to seed Monte Carlo MLE for exponential-family random graph models," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 149-161.
    9. Handcock, Mark S. & Hunter, David R. & Butts, Carter T. & Goodreau, Steven M. & Morris, Martina, 2008. "statnet: Software Tools for the Representation, Visualization, Analysis and Simulation of Network Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 24(i01).
    10. Dootika Vats & James M Flegal & Galin L Jones, 2019. "Multivariate output analysis for Markov chain Monte Carlo," Biometrika, Biometrika Trust, vol. 106(2), pages 321-337.
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    Cited by:

    1. Duncan A. Clark & Mark S. Handcock, 2022. "Comparing the real‐world performance of exponential‐family random graph models and latent order logistic models for social network analysis," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(2), pages 566-587, April.
    2. Juan Li & Keyin Liu & Zixin Yang & Yi Qu, 2023. "Evolution and Impacting Factors of Global Renewable Energy Products Trade Network: An Empirical Investigation Based on ERGM Model," Sustainability, MDPI, vol. 15(11), pages 1-27, May.

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