Cascade of failures in coupled network systems with multiple support-dependent relations

By Jia Shao, Sergey V. Buldyrev, Shlomo Havlin, H. Eugene Stanley. Physical review. E, Statistical, nonlinear, and soft matter physics, 2010

382 citations recorded by the source corpus.

We study, both analytically and numerically, the cascade of failures in two coupled network systems A and B, where multiple support-dependence relations are randomly built between nodes of networks A and B. In our model we assume that each node in one network can function only if it has at least a single support link connecting it to a functional node in the other network. We assume that networks A and B have (i) sizes N{A} and N{B}, (ii) degree distributions of connectivity links P{A}(k) and P{B}(k), (iii) degree distributions of support links P̃{A}(k) and P̃{B}(k), and (iv) random attack removes (1-R{A})N{A} and (1-R{B})N{B} nodes form the networks A and B, respectively. We find the fractions of nodes μ{∞}{A} and μ{∞}{B} which remain functional (giant component) at the end of the cascade process in networks A and B in terms of the generating functions of the degree distributions of their connectivity and support links. In a special case of Erdős-Rényi networks with average degrees a and b in networks A and B, respectively, and Poisson distributions of support links with average degrees ã and b̃ in networks A and B, respectively, μ{∞}{A}=R{A}[1-exp(-ãμ{∞}{B})][1-exp(-aμ{∞}{A})] and μ{∞}{B}=R{B}[1-exp(-b̃μ{∞}{A})][1-exp(-bμ{∞}{B})]. In the limit of ã→∞ and b̃→∞, both networks become independent, and our model becomes equivalent to a random attack on a single Erdős-Rényi network. We also test our theory on two coupled scale-free networks, and find good agreement with the simulations.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/83996ebd625fb51f13d41b8d522a15b7908acf16

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Citations in the corpus

Network resilience (2020, background): “between systems into consideration, many studies have been carried out to study the robustness in interdependent networks [14, 810, 811, 812, 813, 814, 815, 816, 648, 619, 817, 818], interconnected networks [819, 820, 649], multi-layered networks [821, 822, 823, 824, 825], multiplex networks [826], ”
Multilayer networks (2013, background): “, have been removed in the percolation process) [296].”
Networks formed from interdependent networks (2011, background): “2), excludes configurations that completely collapse even for fully interdependent networks once a single node is removed 78 .”
The structure and dynamics of multilayer networks (2014, background): “[169], it is further allowed to one node in layer α to be interdependent to more than one node in a given layer β, but here (if not explicitly otherwise stated) we make the simplifying assumption that every node in layer α can be interdependent at most to a node in layer β, i.”