Steady state and mean recurrence time for random walks on stochastic temporal networks

TL;DR

This paper analyzes two types of random walks on stochastic temporal networks, revealing how their steady states and recurrence times depend on network structure and interevent-time distributions.

Contribution

It introduces a theoretical framework for active and passive random walks on stochastic temporal networks, highlighting their distinct steady state behaviors and recurrence time dependencies.

Findings

Passive random walk has a uniform steady state density.

Active random walk's steady state depends on node degree and interevent-time distribution.

Mean recurrence time is inversely proportional to node degree for both types.

Abstract

Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of random walks on temporal networks. Here we theoretically study two types of event-driven random walks on a stochastic temporal network model that produces arbitrary distributions of interevent-times. In the so-called active random walk, the interevent-time is reinitialized on all links upon each movement of the walker. In the so-called passive random walk, the interevent-time is only reinitialized on the link that has been used last time, and it is a type of correlated random walk. We find that the steady state is always the uniform density for the passive random walk. In contrast, for the active random walk, it increases or decreases with the node's degree depending on the distribution of interevent-times. The mean recurrence time of a node is inversely proportional to the degree for both active and passive random walks. Furthermore, the mean recurrence time does or does not depend on the distribution of interevent-times for the active and passive random walks, respectively.