Abstract
Many real systems such as, roads, shipping routes, and infrastructure systems can be modeled based on spatially embedded networks. The inter-links between two distant spatial networks, such as those formed by transcontinental airline flights, play a crucial role in optimizing communication and transportation over such long distances. Still, little is known about how inter-links affect the structural resilience of such systems. Here, we develop a framework to study the structural resilience of interlinked spatially embedded networks based on percolation theory. We find that the inter-links can be regarded as an external field near the percolation phase transition, analogous to a magnetic field in a ferromagnetic-paramagnetic spin system. By defining the analogous critical exponents δ and γ, we find that their values for various inter-links structures follow Widom's scaling relations. Furthermore, we study the optimal robustness of our model and compare it with the analysis of real-world networks. The framework presented here not only facilitates the understanding of phase transitions with external fields in complex networks but also provides insight into optimizing real-world infrastructure networks.
Original language | English |
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Article number | 093003 |
Journal | New Journal of Physics |
Volume | 20 |
Issue number | 9 |
DOIs | |
State | Published - Sep 2018 |
Bibliographical note
Publisher Copyright:© 2018 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft.
Funding
We acknowledge the BIU Center for Research in Applied Cryptography and Cyber Security, Italy-Israel project OPERA, the Israel-Italian collaborative project NECST, the Israel Science Foundation, the Major Program of National Natural Science Foundation of China (Grants 71690242, 91546118), ONR, Japan Science Foundation, BSF-NSF, and DTRA (Grant no. HDTRA-1-10-1-0014) for financial support. This work was partially supported by the National Natural Science Foundation of China (Grants 61403171, 71403105, 2015M581738 and 1501100B) and Key Research Program of Frontier Sciences, CAS, Grant No. QYZDJ-SSW-SYS019. JF thanks the fellowship program funded by the Planning and Budgeting Committee of the Council for Higher Education of Israel.
Funders | Funder number |
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BSF-NSF | 1501100B, 71403105, 61403171, 2015M581738, HDTRA-1-10-1-0014 |
Japan Science Foundation | |
Key Research Program of Frontier Sciences, CAS | |
Office of Naval Research | |
National Natural Science Foundation of China | 91546118, 71690242 |
Israel Science Foundation | |
Council for Higher Education |
Keywords
- community structure
- external field
- percolation
- resilience
- spatial networks