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

• Published in: New journal of physics 2018-09, Vol.20 (9), p.93003
• Main Authors: Fan, Jingfang, Dong, Gaogao, Shekhtman, Louis M, Zhou, Dong, Meng, Jun, Chen, Xiaosong, Havlin, Shlomo
• Format: Article
• Language: English
• Subjects: community structure; Embedded systems; external field; Ferromagnetism; Infrastructure; Links; Optimization; percolation; Percolation theory; Phase transitions; Physics; Resilience; spatial networks
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/aadceb

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.