Random Walks on Stochastic Temporal Networks

TL;DR

This paper introduces a mathematical framework for analyzing random walks on stochastic temporal networks, capturing the effects of temporal edge patterns on network dynamics and steady states.

Contribution

It develops a stochastic model using waiting-time distributions and derives an exact integro-differential master equation for random walks on temporal networks.

Findings

Exact description of random walks via integro-differential equations

Analytical expression for steady-state distribution

Potential applications in centrality measures for temporal networks

Abstract

In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly understood. In this chapter, we develop a mathematical framework for random walks on temporal networks using an approach that provides a compromise between abstract but unrealistic models and data-driven but non-mathematical approaches. To do this, we introduce a stochastic model for temporal networks in which we summarize the temporal and structural organization of a system using a matrix of waiting-time distributions. We show that random walks on stochastic temporal networks can be described exactly by an integro-differential master equation and derive an analytical expression for its asymptotic steady state. We also discuss how our work might be useful to help build centrality measures for temporal networks.