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Random walks on hypergraphs.

Timoteo Carletti1, Federico Battiston2, Giulia Cencetti3

  • 1Namur Institute for Complex Systems, University of Namur, 5000 Namur, Belgium.

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We introduce a new random walk model for hypergraphs, capturing multibody interactions beyond pairwise links. This approach reveals how higher-order structures influence information diffusion and node ranking in complex systems.

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Area of Science:

  • Network Science
  • Complex Systems
  • Statistical Physics

Background:

  • Traditional network science models pairwise interactions using nodes and edges.
  • Many real-world systems exhibit multibody interactions, better represented by hypergraphs.
  • Existing random walk models are limited to pairwise interactions.

Purpose of the Study:

  • To propose and analyze a novel random walk model on hypergraphs.
  • To understand the impact of higher-order interactions on diffusive processes.
  • To provide a framework for analyzing complex systems with multibody interactions.

Main Methods:

  • Developed a random walk model grounded in a physical model of multibody proximity.
  • Derived an analytical solution for the stationary distribution of walkers.
  • Introduced a generalized random-walk Laplace operator for hypergraphs.

Main Results:

  • The generalized Laplacian reduces to the standard Laplacian for pairwise interactions (hypergraph edges of size 2).
  • Demonstrated the model's applicability on synthetic and real-world hypergraphs.
  • Showcased applications in node ranking within collaboration networks and classification tasks.

Conclusions:

  • Higher-order interactions significantly affect diffusive processes and information spreading in complex networks.
  • The proposed hypergraph random walk model offers a powerful tool for analyzing systems with multibody interactions.
  • This work advances the understanding of network dynamics beyond traditional pairwise approaches.