Work

Approximation for return time distributions of random walks on sparse networks

Year: 2025

Type: article

Abstract: We propose an approximation for the first return time distribution of random walks on undirected networks. We combine a message-passing solution with a mean-field approximation to account for the short- and long-term behaviors, respectively. We test this approximation on several classes of large graphs and find excellent agreement between our approximations and the true distributions. While the statistical properties of a random walk will depend on the structure of the network, the observed agreement between our approximations and numerical calculations implies that while local structure is clearly very influential, global structure is only important in a relatively superficial way, namely through the total number of edges.

Source: Physical review. E

DOI: 10.1103/physreve.111.064306

Authors: Erik Hormann, Renaud Lambiotte, George T. Cantwell

Institutions: University of Oxford, University of Cambridge

Language: English

Topic: Complex Network Analysis Techniques

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Funders: National Science Foundation, Engineering and Physical Sciences Research Council

Awards: Community Detection And Dynamics in Temporal Networks, DMS-EPSRC The Dynamics and Structure of Multiway Networks, BIGDATA: F: Collaborative Research: Mining for Patterns in Graphs and High-Dimensional Data: Achieving the Limits