https://doi.org/10.1140/epjs/s11734-026-02337-4
Regular Article
Node-weighted recurrence analysis for path dynamics on networks
1
Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, Telegrafenberg A 31, Potsdam, Germany
2
Technical University Berlin, Straße des 17. Juni 135, 10623, Berlin, Germany
3
Institute of Geoscience, University of Potsdam, Karl-Liebknecht-Straße 32, 14476, Potsdam, Germany
4
Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Straße 32, 14476, Potsdam, Germany
a
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Received:
30
January
2026
Accepted:
20
April
2026
Published online:
16
May
2026
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.
© The Author(s) 2026
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