Network of Interdependent Networks: Overview of Theory and Applications

  • Dror Y. Kenett
  • Jianxi Gao
  • Xuqing Huang
  • Shuai Shao
  • Irena Vodenska
  • Sergey V. Buldyrev
  • Gerald Paul
  • H. Eugene Stanley
  • Shlomo Havlin
Part of the Understanding Complex Systems book series (UCS)

Abstract

Complex networks appear in almost every aspect of science and technology. Previous work in network theory has focused primarily on analyzing single networks that do not interact with other networks, despite the fact that many real-world networks interact with and depend on each other. Very recently an analytical framework for studying the percolation properties of interacting networks has been introduced. Here we review the analytical framework and the results for percolation laws for a network of networks (NON) formed by \(n\) interdependent random networks. The percolation properties of a network of networks differ greatly from those of single isolated networks. In particular, although networks with broad degree distributions, e.g., scale-free networks, are robust when analyzed as single networks, they become vulnerable in a NON. Moreover, because the constituent networks of a NON are connected by node dependencies, a NON is subject to cascading failure. When there is strong interdependent coupling between networks, the percolation transition is discontinuous (is a first-order transition), unlike the well-known continuous second-order transition in single isolated networks. We also review some possible real-world applications of NON theory.

Notes

Acknowledgments

We wish to thank ONR (Grant N00014-09-1-0380, Grant N00014-12-1-0548), DTRA (Grant HDTRA-1-10-1- 0014, Grant HDTRA-1-09-1-0035), NSF (Grant CMMI 1125290), the European EPIWORK, MULTIPLEX, CONGAS (Grant FP7-ICT-2011-8-317672), FET Open Project FOC 255987 and FOC-INCO 297149, and LINC projects, DFG, the Next Generation Infrastructure (Bsik) and the Israel Science Foundation for financial support. SVB acknowledges the Dr. Bernard W. Gamson Computational Science Center at Yeshiva College.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Dror Y. Kenett
    • 1
  • Jianxi Gao
    • 1
    • 2
    • 3
  • Xuqing Huang
    • 1
  • Shuai Shao
    • 1
  • Irena Vodenska
    • 4
  • Sergey V. Buldyrev
    • 5
  • Gerald Paul
    • 1
  • H. Eugene Stanley
    • 1
  • Shlomo Havlin
    • 6
  1. 1.Center for Polymer Studies, Department of PhysicsBoston universityBostonUSA
  2. 2.Department of AutomationShanghai Jiao Tong, UniversityShanghai People’s Republic of China
  3. 3.Center for Complex Network Research and Department of PhysicsNortheastern UniversityBostonUSA
  4. 4.Administrative Sciences Department, Metropolitan CollegeBoston UniversityBostonUSA
  5. 5.Department of PhysicsYeshiva UniversityNew YorkUSA
  6. 6.Department of PhysicsBar-Ilan UniversityRamat GanIsrael

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