Eradicating catastrophic collapse in interdependent networks via reinforced nodes

Xin Yuan, Yanqing Hu, H. Eugene Stanley, Shlomo Havlin

Research output: Contribution to journalArticlepeer-review

110 Scopus citations

Abstract

In interdependent networks, it is usually assumed, based on percolation theory, that nodes become nonfunctional if they lose connection to the network giant component. However, in reality, some nodes, equipped with alternative resources, together with their connected neighbors can still be functioning after disconnected from the giant component. Here, we propose and study a generalized percolation model that introduces a fraction of reinforced nodes in the interdependent networks that can function and support their neighborhood. We analyze, both analytically and via simulations, the order parameter-the functioning component-comprising both the giant component and smaller components that include at least one reinforced node. Remarkably, it is found that, for interdependent networks, we need to reinforce only a small fraction of nodes to prevent abrupt catastrophic collapses. Moreover, we find that the universal upper bound of this fraction is 0.1756 for two interdependent Erdos-Rényi (ER) networks: regular random (RR) networks and scale-free (SF) networks with large average degrees. We also generalize our theory to interdependent networks of networks (NONs). These findings might yield insight for designing resilient interdependent infrastructure networks.

Original languageEnglish
Pages (from-to)3311-3315
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Volume114
Issue number13
DOIs
StatePublished - 28 Mar 2017

Bibliographical note

Funding Information:
We thank the financial support of the Office of Naval Research Grants N00014-09-1-0380, N00014-12-1-0548, N62909-16-1-2170, and N62909-14-1-N019; Defense Threat Reduction Agency Grants HDTRA- 1-10-1-0014 and HDTRA-1-09-1-0035; National Science Foundation Grants PHY-1505000, CHE-1213217, and CMMI 1125290; Department of Energy Contract DE-AC07-05Id14517; and US-Israel Binational Science Foundation-National Science Foundation Grant 2015781. Y.H. is supported by National Natural Science Foundation of China Grant 61203156, the Hundred-Talent Program of the Sun Yat-sen University, and the Chinese Fundamental Research Funds for the Central Universities Grant 16lgjc84. Financial support was also provided by the European Multiplex and Dynamics and Coevolution in Multilevel Strategic Interaction Games (CONGAS) Projects; the Israel Ministry of Science and Technology with the Italy Ministry of Foreign Affairs; the Next Generation Infrastructure (Bsik); and the Israel Science Foundation. We also thank the Forecasting Financial Crises (FOC) Program of the European Union for support.

Funding

We thank the financial support of the Office of Naval Research Grants N00014-09-1-0380, N00014-12-1-0548, N62909-16-1-2170, and N62909-14-1-N019; Defense Threat Reduction Agency Grants HDTRA- 1-10-1-0014 and HDTRA-1-09-1-0035; National Science Foundation Grants PHY-1505000, CHE-1213217, and CMMI 1125290; Department of Energy Contract DE-AC07-05Id14517; and US-Israel Binational Science Foundation-National Science Foundation Grant 2015781. Y.H. is supported by National Natural Science Foundation of China Grant 61203156, the Hundred-Talent Program of the Sun Yat-sen University, and the Chinese Fundamental Research Funds for the Central Universities Grant 16lgjc84. Financial support was also provided by the European Multiplex and Dynamics and Coevolution in Multilevel Strategic Interaction Games (CONGAS) Projects; the Israel Ministry of Science and Technology with the Italy Ministry of Foreign Affairs; the Next Generation Infrastructure (Bsik); and the Israel Science Foundation. We also thank the Forecasting Financial Crises (FOC) Program of the European Union for support.

FundersFunder number
Israel Ministry of Science and Technology
Next Generation Infrastructure
US-Israel Binational Science Foundation-National Science Foundation2015781
National Science FoundationPHY-1505000, CMMI 1125290, CHE-1213217
Office of Naval ResearchN00014-09-1-0380, N00014-12-1-0548, N62909-16-1-2170, N62909-14-1-N019
U.S. Department of EnergyDE-AC07-05Id14517
Directorate for Engineering1125290
Defense Threat Reduction AgencyHDTRA- 1-10-1-0014, HDTRA-1-09-1-0035
European Commission
National Natural Science Foundation of China61203156
Sun Yat-Sen University
Israel Science Foundation
Ministry for Foreign Affairs
Fundamental Research Funds for the Central Universities16lgjc84

    Keywords

    • Collapse
    • Interdependent networks
    • Percolation
    • Phase transition

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