The effect of spatiality on multiplex networks

Michael M. Danziger, Louis M. Shekhtman, Yehiel Berezin, Shlomo Havlin

Research output: Contribution to journalArticlepeer-review

42 Scopus citations

Abstract

Many multiplex networks are embedded in space, with links more likely to exist between nearby nodes than distant nodes. For example, interdependent infrastructure networks can be represented as multiplex networks, where each layer has links among nearby nodes. Here, we model the effect of spatiality on the robustness of a multiplex network embedded in 2-dimensional space, where links in each layer are of variable but constrained length. Based on empirical measurements of real-world networks, we adopt exponentially distributed link lengths with characteristic length ζ. By changing ζ, we modulate the strength of the spatial embedding. When ζ → ∞, all link lengths are equally likely, and the spatiality does not affect the topology. However, when only short links are allowed, and the topology is overwhelmingly determined by the spatial embedding. We find that, though longer links strengthen a single-layer network, they make a multi-layer network more vulnerable. We further find that when ζ is longer than a certain critical value, , abrupt, discontinuous transitions take place, while for the transition is continuous, indicating that the risk of abrupt collapse can be eliminated if the typical link length is shorter than .

Original languageEnglish
Article number36002
JournalEPL
Volume115
Issue number3
DOIs
StatePublished - Aug 2016

Bibliographical note

Publisher Copyright:
© CopyrightEPLA, 2016.

Funding

The authors acknowledge the MULTIPLEX (No. 317532) EU project, the Israel Science Foundation, Israel Ministry of Science and Technology (MOST) with the Italy Ministry of Foreign Affairs, MOST with the Japan Science and Technology Agency, ONR and DTRA for financial support. The authors also thank Sergey V. Buldyrev for helpful discussions and comments on the model. MMD thanks the Azrieli Foundation for the award of an Azrieli Fellowship grant. The authors thank the anonymous reviewers for helpful comments, especially the verification of the overlap results with a Riemann sum.

FundersFunder number
MULTIPLEX
Office of Naval Research
Defense Threat Reduction Agency
Seventh Framework Programme317532
Japan Science and Technology Agency
Ministry of Foreign Affairs
Israel Science Foundation
Ministry of Science and Technology, Taiwan
Azrieli Foundation
Ministry of science and technology, Israel

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