From unbiased to maximal-entropy random walks on hypergraphs

Traversa, Pietro ; Ferraz de Arruda, Guilherme ; Moreno, Yamir (Universidad de Zaragoza)

Resumen: Random walks have been intensively studied on regular and complex networks, which are used to represent pairwise interactions. Nonetheless, recent works have demonstrated that many real-world processes are better captured by higher-order relationships, which are naturally represented by hypergraphs. Here we study random walks on hypergraphs. Due to the higher-order nature of these mathematical objects, one can define more than one type of walks. In particular, we study the unbiased and the maximal entropy random walk on hypergraphs with two types of steps, emphasizing their similarities and differences. We characterize these dynamic processes by examining their stationary distributions and associated hitting times. To illustrate our findings, we present a toy example and conduct extensive analyses of artificial and real hypergraphs, providing insights into both their structural and dynamical properties. We hope that our findings motivate further research extending the analysis to different classes of random walks as well as to practical applications.

Idioma: Inglés

DOI: 10.1103/PhysRevE.109.054309

Año: 2024

Publicado en: Physical Review E 109, 5 (2024), 054309 [15 pp.]
ISSN: 2470-0045

Factor impacto JCR: 2.4 (2024)

Categ. JCR: PHYSICS, MATHEMATICAL rank: 13 / 61 = 0.213 (2024) - Q1 - T1
Categ. JCR: PHYSICS, FLUIDS & PLASMAS rank: 17 / 41 = 0.415 (2024) - Q2 - T2

Factor impacto SCIMAGO: 0.705 - Condensed Matter Physics (Q2) - Statistics and Probability (Q2) - Statistical and Nonlinear Physics (Q2)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E36-23R-FENOL
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2020-115800GB-I00
Financiación: info:eu-repo/grantAgreement/ES/UZ/UZ-SANTANDER/2020-0274

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Física Teórica (Dpto. Física Teórica)