Response to targeted perturbations for random walks on networks

TL;DR

This paper presents a framework to quantify how local network perturbations affect the mean first-passage time of random walks, revealing size-independent effects and significant impacts in large networks.

Contribution

A novel general framework for analyzing the response of random walk transport metrics to local network perturbations, applicable to various network modifications.

Findings

Relative variation of MFPT is independent of network size.

Targeted perturbations significantly affect transport even in large networks.

Impact depends on geometric parameters and perturbation intensity.

Abstract

We introduce a general framework, applicable to a broad class of random walks on networks, that quantifies the response of the mean first-passage time to a target node to a local perturbation of the network, both in the context of attacks (damaged link) or strategies of transport enhancement (added link). This approach enables to determine explicitly the dependence of this response on geometric parameters (such as the network size and the localization of the perturbation) and on the intensity of the perturbation. In particular, it is showed that the relative variation of the MFPT is independent of the network size, and remains significant in the large size limit. Furthermore, in the case of non compact exploration of the network, it is found that a targeted perturbation keeps a substantial impact on transport properties for any localization of the damaged link.