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The event graph representation of temporal networks suggests that theconnectivity of temporal structures can be mapped to a directed percolationproblem. However, similar to percolation theory on static networks, thismapping is valid under the approximation that the structure and interactiondynamics of the temporal network are determined by its local properties, andotherwise, it is maximally random. We challenge these conditions anddemonstrate the robustness of this mapping in case of more complicated systems.We systematically analyze random and regular network topologies andheterogeneous link-activation processes driven by bursty renewal orself-exciting processes using numerical simulation and finite-size scalingmethods. We find that the critical percolation exponents characterizing thetemporal network are not sensitive to many structural and dynamical networkheterogeneities, while they recover known scaling exponents characterizingdirected percolation on low dimensional lattices. While it is not possible todemonstrate the validity of this mapping for all temporal network models, ourresults establish the first batch of evidence supporting the robustness of thescaling relationships in the limited-time reachability of temporal networks.

Directed Percolation in Random Temporal Network Models with Heterogeneities