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Bogumił Kamiński1, Valérie Poulin2, Paweł Prałat3

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This study introduces a new hypergraph modularity function to measure network clustering, generalizing graph methods. It improves upon existing techniques by reducing hyperedge cuts in network analysis.

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Area of Science:

  • Network Science
  • Graph Theory
  • Data Mining

Background:

  • Hypergraphs are powerful for modeling complex systems but lack developed theoretical foundations and algorithms.
  • Existing network clustering methods, like graph modularity, are not directly applicable to hypergraphs.

Purpose of the Study:

  • To propose a generalized hypergraph modularity function for network clustering.
  • To establish theoretical foundations for optimizing this new function.
  • To develop and test a heuristic algorithm for hypergraph clustering.

Main Methods:

  • Generalizing the Chung-Lu model from graphs to hypergraphs.
  • Defining a hypergraph modularity function.
  • Developing theoretical frameworks for optimization.
  • Implementing and applying a heuristic algorithm.

Main Results:

  • A novel hypergraph modularity function is proposed and theoretically supported.
  • A heuristic algorithm demonstrates practical application.
  • The proposed method reduces hyperedge cuts compared to using the 2-section graph's modularity.

Conclusions:

  • The new hypergraph modularity function offers a robust way to analyze network clustering.
  • This work provides essential theoretical and algorithmic tools for hypergraph-based network analysis.
  • The proposed approach is more effective in preserving network structure than graph-based methods.