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Exponential random graph models for networks with community structure.

Piotr Fronczak1, Agata Fronczak, Maksymilian Bujok

  • 1Faculty of Physics, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Traditional network models fail to capture community structure, limiting their use in algorithm testing. This study introduces an exponential random graph model to accurately represent networks with communities, improving benchmark graph utility.

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Area of Science:

  • Network science
  • Graph theory
  • Statistical modeling

Background:

  • Real-world networks exhibit community structure, a key organizational feature.
  • Existing network models inadequately represent community structure, hindering their use as benchmarks for community detection algorithms.
  • This limitation affects the prediction of various network properties.

Purpose of the Study:

  • To develop an improved network model that accurately captures community structure.
  • To provide a robust benchmark for evaluating community detection algorithms.
  • To enhance the predictive power of network models for real-world systems.

Main Methods:

  • Utilized an exponential random graph model approach.
  • Built upon the theoretical framework of blockmodels.
  • Analyzed both classical and degree-corrected blockmodels.

Main Results:

  • The proposed exponential random graph model successfully incorporates community structure.
  • The degree-corrected blockmodel exhibits a notable node degree scaling property, similar to fractal networks.
  • Analytical studies of blockmodel properties were conducted.

Conclusions:

  • The developed model offers a more realistic representation of networks with community structure.
  • This model serves as a valuable benchmark for community detection algorithms.
  • The findings contribute to a better understanding of network organization and properties.