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We developed a fast algorithm for maximum likelihood estimation (MLE) in complex networks, called equilibrium expectation (EE). This method enables the analysis of much larger networks than previously possible, including large biological and social networks.

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Area of Science:

  • Network science
  • Statistical modeling
  • Computational complexity

Background:

  • Statistical models for complex networks face challenges with increasing network size.
  • Current methods limit empirical analysis to smaller networks.

Purpose of the Study:

  • To propose a fast algorithm for maximum likelihood estimation (MLE) in large network datasets.
  • To enable direct empirical analysis of significantly larger networks.

Main Methods:

  • Developed the equilibrium expectation (EE) algorithm, leveraging Markov chain properties at equilibrium.
  • Applied the EE algorithm to exponential random graph models (ERGM).

Main Results:

  • The EE algorithm significantly increases the size of networks amenable to ERGM analysis.
  • Demonstrated performance on biological and social networks, including one with over 100,000 nodes.

Conclusions:

  • The EE algorithm overcomes computational limitations of previous methods.
  • Facilitates the empirical scope of ERGMs to previously intractable network sizes.