Random walks and search in time-varying networks

TL;DR

This paper investigates the behavior of random walks in time-varying networks, revealing how dynamic connectivity patterns significantly influence search and diffusion processes.

Contribution

It introduces a model for random walks in networks with synchronized dynamics and derives asymptotic solutions, highlighting differences from static network results.

Findings

Distinct asymptotic behaviors in time-varying networks

Impact of network dynamics on mean first passage time

Differences from quenched and annealed network models

Abstract

The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity pattern and the random walk process dynamics are unfolding on the same time scale. We consider a model for time varying networks created from the activity potential of the nodes, and derive solutions of the asymptotic behavior of random walks and the mean first passage time in undirected and directed networks. Our findings show striking differences with respect to the well known results obtained in quenched and annealed networks, emphasizing the effects of dynamical connectivity patterns in the definition of proper strategies for search, retrieval and diffusion processes in time-varying networks