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From unbiased to maximal-entropy random walks on hypergraphs.

Pietro Traversa^1,2,3, Guilherme Ferraz de Arruda³, Yamir Moreno^1,2,3

¹Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, 50018 Zaragoza, Spain.

Physical Review. E

|June 22, 2024

Summary

This study introduces random walks on hypergraphs, exploring unbiased and maximal entropy types. Analyzing stationary distributions and hitting times reveals key structural and dynamical properties of these complex systems.

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Area of Science:

Mathematics
Network Science
Statistical Physics

Background:

Random walks are crucial for analyzing pairwise interactions in networks.
Real-world processes often involve higher-order relationships better modeled by hypergraphs.
Existing random walk models do not fully capture hypergraph complexity.

Purpose of the Study:

To investigate random walks on hypergraphs, a structure for higher-order relationships.
To define and compare unbiased and maximal entropy random walks on hypergraphs.
To analyze the structural and dynamical properties of hypergraphs using these random walk models.

Main Methods:

Defining and analyzing two types of random walks: unbiased and maximal entropy.
Examining stationary distributions of these random walks.
Calculating and comparing associated hitting times.
Illustrating with a toy example and analyzing artificial and real hypergraphs.

Main Results:

Characterization of unbiased and maximal entropy random walks on hypergraphs.
Identification of similarities and differences between the two walk types.
Insights into the structural and dynamical properties of hypergraphs derived from random walk analysis.

Conclusions:

Random walks on hypergraphs offer a powerful framework for studying complex systems with higher-order interactions.
The study provides a foundation for further research into diverse random walk models and applications on hypergraphs.
Findings contribute to understanding both the structure and dynamics of systems represented by hypergraphs.