Random walks on temporal networks

TL;DR

This paper investigates how random walks behave on evolving temporal networks, revealing that temporal correlations slow exploration and that network duration impacts dynamics, providing insights into processes on real-world dynamic systems.

Contribution

It introduces empirical analysis and randomization strategies to understand the impact of temporal properties on random walks in evolving networks, highlighting the role of temporal correlations.

Findings

Random walks are slower on temporal networks than on aggregated networks.

Temporal correlations between contacts significantly influence exploration speed.

Limited network duration affects the dynamics of processes on temporal networks.

Abstract

Many natural and artificial networks evolve in time. Nodes and connections appear and disappear at various timescales, and their dynamics has profound consequences for any processes in which they are involved. The first empirical analysis of the temporal patterns characterizing dynamic networks are still recent, so that many questions remain open. Here, we study how random walks, as paradigm of dynamical processes, unfold on temporally evolving networks. To this aim, we use empirical dynamical networks of contacts between individuals, and characterize the fundamental quantities that impact any general process taking place upon them. Furthermore, we introduce different randomizing strategies that allow us to single out the role of the different properties of the empirical networks. We show that the random walk exploration is slower on temporal networks than it is on the aggregate projected network, even when the time is properly rescaled. In particular, we point out that a fundamental role is played by the temporal correlations between consecutive contacts present in the data. Finally, we address the consequences of the intrinsically limited duration of many real world dynamical networks. Considering the fundamental prototypical role of the random walk process, we believe that these results could help to shed light on the behavior of more complex dynamics on temporally evolving networks.