Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 113, Issue 5, Pages 1138-1143Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1523412113
Keywords
interdependent networks; directed networks; degree correlations; percolation theory
Categories
Funding
- National Science Foundation [PHY-1505000, CMMI 1125290]
- National Institutes of Health [5R01AG021133]
- Department of Defense [HDTRA1-14-1-017]
- Office of Naval Research [N00014-14-1-0738]
- Department of Energy [DE-AC07-051D14517]
- Army Research Laboratory (ARL) [W911NF-09-2-0053]
- John Templeton Foundation [PFI-777]
- Defense Threat Reduction Agency [HDTRA1-10-1-0100]
- European Commission [FP7317532, 641191]
- National Natural Science Foundation of China [61320106005, 91530320, 61374160]
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [1125290] Funding Source: National Science Foundation
- Division Of Physics
- Direct For Mathematical & Physical Scien [1504804, 1505000] Funding Source: National Science Foundation
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Increasing evidence shows that real-world systems interact with one another via dependency connectivities. Failing connectivities are the mechanism behind the breakdown of interacting complex systems, e.g., blackouts caused by the interdependence of power grids and communication networks. Previous research analyzing the robustness of interdependent networks has been limited to undirected networks. However, most real-world networks are directed, their in-degrees and out-degrees may be correlated, and they are often coupled to one another as interdependent directed networks. To understand the breakdown and robustness of interdependent directed networks, we develop a theoretical framework based on generating functions and percolation theory. We find that for interdependent Erdos-Renyi networks the directionality within each network increases their vulnerability and exhibits hybrid phase transitions. We also find that the percolation behavior of interdependent directed scale-free networks with and without degree correlations is so complex that two criteria are needed to quantify and compare their robustness: the percolation threshold and the integrated size of the giant component during an entire attack process. Interestingly, we find that the in-degree and out-degree correlations in each network layer increase the robustness of interdependent degree heterogeneous networks that most real networks are, but decrease the robustness of interdependent networks with homogeneous degree distribution and with strong coupling strengths. Moreover, by applying our theoretical analysis to real interdependent international trade networks, we find that the robustness of these real-world systems increases with the in-degree and out-degree correlations, confirming our theoretical analysis.
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