Critical Stretching of Mean-Field Regimes in Spatial Networks

Ivan Bonamassa, Bnaya Gross, Michael M. Danziger, Shlomo Havlin

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We study a spatial network model with exponentially distributed link lengths on an underlying grid of points, undergoing a structural crossover from a random, Erdos-Rényi graph, to a d-dimensional lattice at the characteristic interaction range ζ. We find that, whilst far from the percolation threshold the random part of the giant component scales linearly with ζ, close to criticality it extends in space until the universal length scale ζ6/(6-d), for d<6, before crossing over to the spatial one. We demonstrate the universal behavior of the spatiotemporal scales characterizing this critical stretching phenomenon of mean-field regimes in percolation and in dynamical processes on d=2 networks, and we discuss its general implications to real-world phenomena, such as neural activation, traffic flows or epidemic spreading.

Original languageEnglish
Article number088301
Number of pages5
JournalPhysical Review Letters
Issue number8
StatePublished - 22 Aug 2019

Bibliographical note

Funding Information:
I.-B. and B.-G. contributed equally to this work. S.-H. acknowledges financial support from the ISF, ONR, DTRA: HDTRA-1-10-1-0014, BSF-NSF: 2015781, ARO, the Israeli Ministry of Science, Technology and Space (MOST) in joint collaboration with the Japan Science Foundation (JSF), and the Italian Ministry of Foreign Affairs and International Cooperation (MAECI), and the Bar-Ilan University Center for Research in Applied Cryptography and Cyber Security. I.-B. thanks S.-V. Buldyrev, G. Sicuro, and M.-C. Strinati for valuable discussions.

Publisher Copyright:
© 2019 American Physical Society.


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