Node-weighted recurrence analysis for path dynamics on networks

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.