The extreme vulnerability of interdependent spatially embedded networks

By Amir Bashan, Yehiel Berezin, Sergey V. Buldyrev, Shlomo Havlin. Nature Physics, 2012

307 citations recorded by the source corpus.

Recent studies show that in interdependent networks a very small failure in one network may lead to catastrophic consequences. Above a critical fraction of interdependent nodes, even a single node failure can invoke cascading failures that may abruptly fragment the system, whereas below this critical dependency a failure of a few nodes leads only to a small amount of damage to the system. So far, research has focused on interdependent random networks without space limitations. However, many real systems, such as power grids and the Internet, are not random but are spatially embedded. Here we analytically and numerically study the stability of interdependent spatially embedded networks modelled as lattice networks. Surprisingly, we find that in lattice systems, in contrast to non-embedded systems, there is no critical dependency and any small fraction of interdependent nodes leads to an abrupt collapse. We show that this extreme vulnerability of very weakly coupled lattices is a consequence of the critical exponent describing the percolation transition of a single lattice. Networks of networks are vulnerable: a failure in one sub-network can bring the rest crashing down. Previous simulations have suggested that randomly positioned networks might offer some limited robustness under certain circumstances. Analysis now shows, however, that real-world interdependent networks, where nodes are positioned according to geographical constraints, might not be so resilient.

Subfields: Civil and Structural Engineering, Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4a866a3342755a3403a4f4d886ed6e5cea2c135f

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In Civil and Structural Engineering

In Computer Networks and Communications

In Statistical and Nonlinear Physics

Citations in the corpus

Multilayer networks (2013, methodology): “In some cases, it is desirable to disregard the weights of a monoplex network that one obtains by aggregating multiplex networks and to instead examine an unweighted monoplex network [34, 75, 76, 309] (References [95, 309] used the term “projected network” to describe this situation, though it is pr”
The structure and dynamics of multilayer networks (2014, background): “[189] partial interdependence was considered, and the Authors found that, in contrast to unembedded networks, for any fraction of dependency links the system collapses in an abrupt transition.”
Synchronous failure: the emerging causal architecture of global crisis (2015, background): “…creates tight coupling among these components, which raises the risk of surprising and harmful interactions among them (Perrow 1999) and of localized failures spreading quickly to other, distant system components (Buldyrev et al. 2010, Harmon et al. 2010, Bashan et al. 2013, Helbing 2013).”
Data Based Identification and Prediction of Nonlinear and Complex Dynamical Systems (2016, background): “binary-state dynamics on complex networks [42], such as the voter models for competition of two opinions [438], stochastic propagation models for epidemic spreading [439], models of rumor diffusion and adoption of new technologies [440], cascading failure models [441], Ising spin models for ferromag”
Robustness and resilience of complex networks (2024, background): “…on the structural features of a system (such as whether it is spatially embedded or not, interdependent with other systems or not, or multiplex 34–36 ) and its dynamics (for instance, whether it has regimes in which collective behaviour emerges, such as in synchronization, epidemic spreading…”
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], ”