Directed percolation in random temporal network models with heterogeneities

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Physical Review E, Volume 105, issue 5
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.
| openaire: EC/H2020/871042/EU//SoBigData-PlusPlus Funding Information: We thank János Kertész and Géza Ódor for their helpful comments and suggestions. The authors acknowledge the CSC–IT Center for Science, Finland, and Aalto University “Science-IT” project for generous computational resources. Márton Karsai acknowledges support from the DataRedux ANR project (ANR-19-CE46-0008) and the SoBigData++ H2020 project (H2020-871042). Publisher Copyright: © 2022 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
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Badie-Modiri, A, Rizi, A K, Karsai, M & Kivelä, M 2022, ' Directed percolation in random temporal network models with heterogeneities ', Physical Review E, vol. 105, no. 5, 054313, pp. 1-17 .