Random walks on complex networks with multiple resetting nodes: a renewal approach

TL;DR

This paper develops a renewal approach to analyze discrete-time random walks with multiple resetting nodes on complex networks, deriving exact occupation probabilities and first-passage times, and demonstrating advantages in network searching.

Contribution

Introduces a renewal-based method to exactly analyze random walks with multiple resetting nodes on complex networks, linking results to spectral properties.

Findings

Resetting improves global search efficiency on various networks.

Derived exact formulas for occupation probabilities and mean first-passage times.

Demonstrated advantages of multiple resetting nodes in complex network exploration.

Abstract

Due to wide applications in diverse fields, random walks subject to stochastic resetting have attracted considerable attention in the last decade. In this paper, we study discrete-time random walks on complex network with multiple resetting nodes. Using a renewal approach, we derive exact expressions of the occupation probability of the walker in each node and mean-field first-passage time between arbitrary two nodes. All the results are relevant to the spectral properties of the transition matrix in the absence of resetting. We demonstrate our results on circular networks, stochastic block models, and Barab\'asi-Albert scale-free networks, and find the advantage of the resetting processes to multiple resetting nodes in global searching on such networks.