Node-weighted recurrence analysis for path dynamics on networks

TL;DR

This paper adapts recurrence quantification analysis (RQA) to study path dynamics on networks, revealing unique recurrence patterns like backtracking, and demonstrating its utility in understanding network structure and dynamics.

Contribution

It introduces a novel application of RQA to network path trajectories, highlighting new recurrence patterns and potential insights into network and path dynamics.

Findings

Path dynamics show unique recurrence patterns, including backtracking.

Recurrence analysis helps understand network structure and dynamics.

The method reveals interactions between path behavior and network topology.

Abstract

Trajectories of units moving on networks are relevant for nonlinear dynamical systems as diverse as polymers, ocean drifters, and human mobility. Although RQA is a well-researched tool with applications in many areas, it has rarely been used for spatial trajectories on networks. Here, we explore the use of RQA for paths on networks. We find that path dynamics on networks display recurrence patterns that are not often described in other applications of recurrence analysis. In particular, the combination of diagonal lines and perpendicular diagonal lines, indicates backtracking paths. We find that recurrence analysis for path dynamics on networks can be helpful to a) better understand the network structure if dynamic and recurrence plots are known, b) better understand the dynamics if network and recurrence plots are known, and c) understand the interaction between path dynamics and the underlying network.