title: Breakdown of interdependent directed networks.
abstract: 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 Erdős-Rényi 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.
authors.affiliation: Key Laboratory of Image Information Processing and Intelligent Control, School of Automation, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China; Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215;
authors.forename: Xueming
authors.initials: X
authors.lastname: Liu
authors.affiliation: Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215; hes@bu.edu jianxi.gao@gmail.com.
authors.forename: H Eugene
authors.initials: HE
authors.lastname: Stanley
authors.affiliation: Center for Complex Network Research and Department of Physics, Northeastern University, Boston, MA 02115 hes@bu.edu jianxi.gao@gmail.com.
authors.forename: Jianxi
authors.initials: J
authors.lastname: Gao
mesh_terms: D003142:Communication; D011211:Electric Power Supplies; D008962:Models, Theoretical
keywords: degree correlations; directed networks; interdependent networks; percolation theory