Comptes Rendus
Robustness of spatial networks and networks of networks
Comptes Rendus. Physique, Volume 19 (2018) no. 4, pp. 233-243.

Many complex networks have recently been recognized to involve significant interdependence between different systems. Motivation comes primarily from infrastructures like power grids and communications networks, but also includes areas such as the human brain and finance. Interdependence implies that when components in one system fail, they lead to failures in the same system or other systems. This can then lead to additional failures finally resulting in a long cascade that can cripple the entire system. Furthermore, many of these networks, in particular infrastructure networks, are embedded in space and thus have unique spatial properties that significantly decrease their resilience to failures. Here we present a review of novel results on interdependent spatial networks and how cascading processes are affected by spatial embedding. We include various aspects of spatial embedding such as cases where dependencies are spatially restricted and localized attacks on nodes contained in some spatial region of the network. In general, we find that spatial networks are more vulnerable when they are interdependent and that they are more likely to undergo abrupt failure transitions than interdependent non-embedded networks. We also present results on recovery in spatial networks, the nature of cascades due to overload failures in these networks, and some examples of percolation features found in real-world traffic networks. Finally, we conclude with an outlook on future possible research directions in this area.

Récemment, il a été montré que de nombreux réseaux complexes font intervenir une interdépendence fondamentale entre différents systèmes. La motivation provient principalement des infrastructures telles que les réseaux électriques et les réseaux de communication, mais comprend également des domaines tels que le cerveau humain et la finance. L'interdépendance implique que, lorsque des composants d'un système tombent en panne, ils entraînent des défaillances dans le même système ou dans d'autres. Cela peut conduire à des défaillances supplémentaires, aboutissant finalement à une longue cascade susceptible de paralyser l'ensemble du système. En outre, nombre de ces réseaux, en particulier certaines infrastructures, sont intégrés dans l'espace et possèdent des propriétés spatiales uniques qui ont pour effet de réduire considérablement leur résilience aux pannes. Nous présentons également des résultats sur la guérison des réseaux spatiaux, la nature des cascades dues à des défaillances de surcharge dans ces réseaux, ainsi que quelques exemples choisis dans les réseaux de trafic réel et qui présentent des caractéristiques similaires à celles de la percolation. Enfin, nous concluons sur une discussion des futures directions de recherche possibles dans ce domaine.

Published online:
DOI: 10.1016/j.crhy.2018.09.005
Keywords: Spatial networks, Networks of networks, Coupled networks, Infrastructure resilience
Mot clés : Réseaux spatiaux, Réseaux de réseaux, Réseaux couplés, Résilience des infrastructures

Louis M. Shekhtman 1; Michael M. Danziger 2; Dana Vaknin 1; Shlomo Havlin 1, 3

1 Department of Physics, Bar-Ilan University, Ramat Gan, Israel
2 Network Science Institute and Department of Physics, Northeastern University, Boston, USA
3 Tokyo Institute of Technology, Tokyo, Japan
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Louis M. Shekhtman; Michael M. Danziger; Dana Vaknin; Shlomo Havlin. Robustness of spatial networks and networks of networks. Comptes Rendus. Physique, Volume 19 (2018) no. 4, pp. 233-243. doi : 10.1016/j.crhy.2018.09.005. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2018.09.005/

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