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Edge Based Stochastic Block Model Statistical Inference

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Complex Networks & Their Applications IX (COMPLEX NETWORKS 2020 2020)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 944))

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Abstract

Community detection in graphs often relies on ad hoc algorithms with no clear specification about the node partition they define as the best, which leads to uninterpretable communities. Stochastic block models (SBM) offer a framework to rigorously define communities, and to detect them using statistical inference method to distinguish structure from random fluctuations. In this paper, we introduce an alternative definition of SBM based on edge sampling. We derive from this definition a quality function to statistically infer the node partition used to generate a given graph. We then test it on synthetic graphs, and on the zachary karate club network.

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Notes

  1. 1.

    https://graph-tool.skewed.de.

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Acknowledgments

This work was supported by the ACADEMICS grant of the IDEXLYON, project of the Université de Lyon, PIA operated by ANR-16-IDEX-0005, and of the project ANR-18-CE23-0004 (BITUNAM) of the French National Research Agency (ANR).

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Authors and Affiliations

  1. Univ Lyon, INSA Lyon, CNRS, LIRIS UMR5205, 69621, Paris, France

    Louis Duvivier & Céline Robardet

  2. Univ Lyon, Université Lyon 1, CNRS, LIRIS UMR5205, 69622, Paris, France

    Rémy Cazabet

Authors
  1. Louis Duvivier
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  2. Rémy Cazabet
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  3. Céline Robardet
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Corresponding author

Correspondence to Louis Duvivier .

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Editors and Affiliations

  1. Grupo de Sistemas Complejos, Universidad Politécnica de Madrid, Madrid, Madrid, Spain

    Rosa M. Benito

  2. IUT Lumière, University of Lyon, Bron Cedex, France

    Chantal Cherifi

  3. LE2I, UFR Sciences et Techniques, Université de Bourgogne, Dijon, France

    Hocine Cherifi

  4. Grupo Interdisciplinar de Sistemas Complejos, Departamento de Matematicas, Universidad Carlos III de Madrid, Leganés, Madrid, Spain

    Esteban Moro

  5. Center for Social and Biomedical Complexity, Luddy School of Informatics, Computing, and Engineering, Indiana University, Bloomington, IN, USA

    Luis Mateus Rocha

  6. Department of Chemical Engineering, Universitat Rovira i Virgili, Tarragona, Tarragona, Spain

    Marta Sales-Pardo

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Duvivier, L., Cazabet, R., Robardet, C. (2021). Edge Based Stochastic Block Model Statistical Inference. In: Benito, R.M., Cherifi, C., Cherifi, H., Moro, E., Rocha, L.M., Sales-Pardo, M. (eds) Complex Networks & Their Applications IX. COMPLEX NETWORKS 2020 2020. Studies in Computational Intelligence, vol 944. Springer, Cham. https://doi.org/10.1007/978-3-030-65351-4_37

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  • DOI: https://doi.org/10.1007/978-3-030-65351-4_37

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-65350-7

  • Online ISBN: 978-3-030-65351-4

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