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

15 Scopus citations


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
Issue number9
StatePublished - 1 Sep 2018
Externally publishedYes


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

ASJC Scopus subject areas

  • General Physics and Astronomy


Dive into the research topics of 'Structural resilience of spatial networks with inter-links behaving as an external field'. Together they form a unique fingerprint.

Cite this