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Exponential random graph model parameter estimation for very large directed networks.

Alex Stivala1,2, Garry Robins3, Alessandro Lomi1,4

  • 1Institute of Computational Science, Università della Svizzera italiana, Lugano, Ticino, Switzerland.

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Summary
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Exponential random graph models (ERGMs) can now estimate parameters for large directed social networks. This new method, the Equilibrium Expectation (EE) algorithm, overcomes previous computational limits for network analysis.

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Area of Science:

  • Network Science
  • Computational Social Science
  • Statistical Modeling

Background:

  • Exponential Random Graph Models (ERGMs) are standard for analyzing social networks.
  • Computational challenges limit ERGM application to small networks (typically <1000 nodes).
  • Existing methods for large undirected networks have scalability and directional limitations.

Purpose of the Study:

  • To implement and evaluate the Equilibrium Expectation (EE) algorithm for large directed network ERGM parameter estimation.
  • To overcome computational limitations of ERGM for large-scale directed network analysis.
  • To demonstrate the algorithm's applicability to real-world, large online social networks.

Main Methods:

  • Implementation of the Equilibrium Expectation (EE) algorithm for directed ERGMs.
  • Testing the algorithm on simulated directed networks.
  • Application to a large-scale online social network dataset (>1.6 million nodes).

Main Results:

  • The EE algorithm implementation successfully estimates ERGM parameters for large directed networks.
  • The method demonstrates scalability beyond previous ERGM estimation techniques.
  • Successful application to a real-world online social network with over 1.6 million nodes.

Conclusions:

  • The developed EE algorithm implementation significantly advances the capability to analyze large directed social networks using ERGMs.
  • This work removes computational barriers, enabling more comprehensive network analysis.
  • Facilitates deeper insights into the structure and dynamics of massive online social systems.