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Network of Interdependent Networks: Overview of Theory and Applications

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Networks of Networks: The Last Frontier of Complexity

Part of the book series: Understanding Complex Systems ((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.

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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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Authors and Affiliations

  1. Center for Polymer Studies, Department of Physics, Boston university, Boston, MA , 02215, USA

    Dror Y. Kenett, Jianxi Gao, Xuqing Huang, Shuai Shao, Gerald Paul & H. Eugene Stanley

  2. Department of Automation, Shanghai Jiao Tong, University, 800 Dongchuan Road, Shanghai , 200240, People’s Republic of China

    Jianxi Gao

  3. Center for Complex Network Research and Department of Physics, Northeastern University, Boston, MA, 02115, USA

    Jianxi Gao

  4. Administrative Sciences Department, Metropolitan College, Boston University, Boston, MA , 02215, USA

    Irena Vodenska

  5. Department of Physics, Yeshiva University, New York, NY, 10033, USA

    Sergey V. Buldyrev

  6. Department of Physics, Bar-Ilan University, Ramat Gan, Israel

    Shlomo Havlin

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  1. Dror Y. Kenett
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  2. Jianxi Gao
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  3. Xuqing Huang
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  4. Shuai Shao
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  6. Sergey V. Buldyrev
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  7. Gerald Paul
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  8. H. Eugene Stanley
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  9. Shlomo Havlin
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Correspondence to Dror Y. Kenett .

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  1. ENEA - Italian National Agency for New Technology, Energy and Sustainable Economic Development, Rome, Italy

    Gregorio D'Agostino

  2. CNR-ISC Uos "La Sapienza", Rome, Italy

    Antonio Scala

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Kenett, D.Y. et al. (2014). Network of Interdependent Networks: Overview of Theory and Applications. In: D'Agostino, G., Scala, A. (eds) Networks of Networks: The Last Frontier of Complexity. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-03518-5_1

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