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Modularity of the ABCD Random Graph Model with Community Structure

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Complex Networks and Their Applications XI (COMPLEX NETWORKS 2016 2022)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 1078))

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Abstract

The Artificial Benchmark for Community Detection graph (ABCD) is a random graph model with community structure and power-law distribution for both degrees and community sizes. The model generates graphs with similar properties as the well-known LFR one, and its main parameter \(\xi \) can be tuned to mimic its counterpart in the LFR model, the mixing parameter \(\mu \). In this paper, we investigate various theoretical asymptotic properties of the ABCD model. In particular, we analyze the modularity function, arguably, the most important graph property of networks in the context of community detection. Indeed, the modularity function is often used to measure the presence of community structure in networks. It is also used as a quality function in many community detection algorithms, including the widely used Louvain algorithm.

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Notes

  1. 1.

    https://github.com/bkamins/ABCDGraphGenerator.jl/.

  2. 2.

    https://github.com/tolcz/ABCDeGraphGenerator.jl/.

  3. 3.

    https://github.com/bkamins/ABCDGraphGenerator.jl/.

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Author information

Authors and Affiliations

  1. Warsaw School of Economics, Warsaw, Poland

    Bogumił Kamiński

  2. Ryerson University, Toronto, ON, Canada

    Bartosz Pankratz & Paweł Prałat

  3. The Tutte Institute for Mathematics and Computing, Ottawa, ON, Canada

    François Théberge

Authors
  1. Bogumił Kamiński
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  2. Bartosz Pankratz
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  3. Paweł Prałat
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  4. François Théberge
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Corresponding author

Correspondence to Paweł Prałat .

Editor information

Editors and Affiliations

  1. University of Burgundy, Dijon, France

    Hocine Cherifi

  2. Dipartimento di Fisica e Chimica—Emilio Segrè, Università degli Studi Palermo, Palermo, Italy

    Rosario Nunzio Mantegna

  3. Thomas J. Watson College of Engineering and Applied Science, Binghamton University, Binghamton, NY, USA

    Luis M. Rocha

  4. IUT Lumière—Université Lyon 2, University of Lyon, Bron, France

    Chantal Cherifi

  5. Dipartimento di Fisica e Chimica—Emilio Segrè, Università degli Studi Palermo, Palermo, Italy

    Salvatore Micciche

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Kamiński, B., Pankratz, B., Prałat, P., Théberge, F. (2023). Modularity of the ABCD Random Graph Model with Community Structure. In: Cherifi, H., Mantegna, R.N., Rocha, L.M., Cherifi, C., Micciche, S. (eds) Complex Networks and Their Applications XI. COMPLEX NETWORKS 2016 2022. Studies in Computational Intelligence, vol 1078. Springer, Cham. https://doi.org/10.1007/978-3-031-21131-7_1

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  • DOI: https://doi.org/10.1007/978-3-031-21131-7_1

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  • Print ISBN: 978-3-031-21130-0

  • Online ISBN: 978-3-031-21131-7

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