Structural resilience of spatial networks with inter-links behaving as an external field

Jingfang Fan, Gaogao Dong, Louis M. Shekhtman, Dong Zhou, Jun Meng, Xiaosong Chen, Shlomo Havlin

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

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 languageEnglish
Article number093003
JournalNew Journal of Physics
Volume20
Issue number9
DOIs
StatePublished - 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.

FundersFunder number
BSF-NSF1501100B, 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 China91546118, 71690242
Israel Science Foundation
Council for Higher Education

    Keywords

    • community structure
    • external field
    • percolation
    • resilience
    • spatial networks

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