First passage time for random walks in heterogeneous networks

TL;DR

This paper investigates the first passage time of random walks in heterogeneous networks, revealing how network structure influences diffusion speed and providing insights for designing efficient information systems.

Contribution

It offers a combined analytical and numerical analysis of FPT behavior in heterogeneous networks, highlighting the effects of local hubs and exploration strategies.

Findings

Random walks reach local hubs quickly, causing a crossover in FPT decay behavior.

Mean FPT is independent of target node degree in compact exploration.

Results support using random jump protocols for efficient information access.

Abstract

The first passage time (FPT) for random walks is a key indicator of how fast information diffuses in a given system. Despite the role of FPT as a fundamental feature in transport phenomena, its behavior, particularly in heterogeneous networks, is not yet fully understood. Here, we study, both analytically and numerically, the scaling behavior of the FPT distribution to a given target node, averaged over all starting nodes. We find that random walks arrive quickly at a local hub, and therefore, the FPT distribution shows a crossover with respect to time from fast decay behavior (induced from the attractive effect to the hub) to slow decay behavior (caused by the exploring of the entire system). Moreover, the mean FPT is independent of the degree of the target node in the case of compact exploration. These theoretical results justify the necessity of using a random jump protocol (empirically used in search engines) and provide guidelines for designing an effective network to make information quickly accessible.