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Clustering via hypergraph modularity

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  • Bogumił Kamiński
  • Valérie Poulin
  • Paweł Prałat
  • Przemysław Szufel
  • François Théberge

Abstract

Despite the fact that many important problems (including clustering) can be described using hypergraphs, theoretical foundations as well as practical algorithms using hypergraphs are not well developed yet. In this paper, we propose a hypergraph modularity function that generalizes its well established and widely used graph counterpart measure of how clustered a network is. In order to define it properly, we generalize the Chung-Lu model for graphs to hypergraphs. We then provide the theoretical foundations to search for an optimal solution with respect to our hypergraph modularity function. A simple heuristic algorithm is described and applied to a few illustrative examples. We show that using a strict version of our proposed modularity function often leads to a solution where a smaller number of hyperedges get cut as compared to optimizing modularity of 2-section graph of a hypergraph.

Suggested Citation

  • Bogumił Kamiński & Valérie Poulin & Paweł Prałat & Przemysław Szufel & François Théberge, 2019. "Clustering via hypergraph modularity," PLOS ONE, Public Library of Science, vol. 14(11), pages 1-15, November.
    • Handle: RePEc:plo:pone00:0224307
    DOI: 10.1371/journal.pone.0224307
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    Cited by:

    1. Chessa, Michela & Persenda, Arnaud & Torre, Dominique, 2023. "Brexit and Canadadvent: An application of graphs and hypergraphs to recent international trade agreements," International Economics, Elsevier, vol. 175(C), pages 1-12.

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