Directed Percolation in Random Temporal Network Models with Heterogeneities

TL;DR

This paper investigates the robustness of the directed percolation mapping in temporal networks with heterogeneities, showing that critical exponents remain consistent despite structural and dynamical complexities.

Contribution

It provides the first systematic analysis demonstrating the robustness of directed percolation scaling in complex, heterogeneous temporal network models.

Findings

Critical exponents are insensitive to network heterogeneities.

Scaling exponents match those of directed percolation on low-dimensional lattices.

The mapping remains valid under various complex network conditions.

Abstract

The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similar to percolation theory on static networks, this mapping is valid under the approximation that the structure and interaction dynamics of the temporal network are determined by its local properties, and otherwise, it is maximally random. We challenge these conditions and demonstrate the robustness of this mapping in case of more complicated systems. We systematically analyze random and regular network topologies and heterogeneous link-activation processes driven by bursty renewal or self-exciting processes using numerical simulation and finite-size scaling methods. We find that the critical percolation exponents characterizing the temporal network are not sensitive to many structural and dynamical network heterogeneities, while they recover known scaling exponents characterizing directed percolation on low dimensional lattices. While it is not possible to demonstrate the validity of this mapping for all temporal network models, our results establish the first batch of evidence supporting the robustness of the scaling relationships in the limited-time reachability of temporal networks.