Directed percolation in random temporal network models with heterogeneities

Arash Badie-Modiri, Abbas K. Rizi, Márton Karsai, Mikko Kivelä

Research output: Contribution to journalArticlepeer-review

Abstract (may include machine translation)

The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similarly 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.

Original languageEnglish
Article number054313
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume105
Issue number5
DOIs
StatePublished - May 2022

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