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Configuration models as an urn problem.

Giona Casiraghi1, Vahan Nanumyan2

  • 1ETH Zürich, Zürich, 8092, Switzerland. gcasiraghi@ethz.ch.

Scientific Reports
|June 29, 2021
PubMed
Summary

Network data science distinguishes random from non-random features using configuration models. We introduce a generalized hypergeometric ensemble, offering a flexible, efficient alternative to standard models for large-scale network analysis.

Area of Science:

  • Network data science
  • Graph theory
  • Statistical modeling

Background:

  • Distinguishing random from non-random network features is crucial.
  • Configuration models serve as null-models but have limitations for large-scale analysis.
  • Existing methods often require computationally expensive simulations or lack flexibility.

Purpose of the Study:

  • To address limitations of existing configuration models for large-scale network data analysis.
  • To develop a novel random graph model with improved efficiency and flexibility.
  • To provide a closed-form probability distribution for enhanced analytical capabilities.

Main Methods:

  • Mapping the configuration model to an urn problem.
  • Developing the generalized hypergeometric ensemble of random graphs.

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  • Deriving a closed-form probability distribution for the ensemble.

    • Main Results:

    • The generalized hypergeometric ensemble reproduces and extends standard configuration model properties.
    • This new model offers a closed-form probability distribution, avoiding Monte Carlo simulations.
    • The ensemble provides a flexible framework for modeling complex real-world networks.

    Conclusions:

    • The generalized hypergeometric ensemble offers a computationally efficient and flexible alternative to existing configuration models.
    • This advancement facilitates more robust analysis of large-scale network data.
    • The closed-form distribution simplifies statistical inference in network science.