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 Erd} os-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.interdependent networks | directed networks | degree correlations | percolation theory

On the Robustness of No-Feedback Interdependent Networks

“…These kinds of interdependent networks were firstly constructed and the percolation process of such systems studied by Parshani in Reference [2]. In addition, there are few bidirectional (or undirected) dependency links similar to those shown as Figure 1a, and most of the dependency links in interdependent networks are directed [23]. For example, a node in the control network may control a power network node, but this power node is not necessarily responsible for the power supply of this control node, i.e., the power node depends on the control node but not vice versa, which constitutes unidirectional dependency.…”

“…Coupling preference determines the way that dependency links are established between subnetworks, such as assortative coupling, disassortative coupling, and random coupling based on node degree or betweenness [21]. The dependency link can be either directed [22,23] or undirected [13,14]. Fu et al [24] investigated the influence of the dependency link direction on the robustness of interdependent networks, and found that the robustness of directed interdependent networks was worse than undirected ones.…”

Robustness and lethality in multilayer biological molecular networks

“…In network science, systems composed of multiple interacting networks [24][25][26][27][28] have attracted considerable attention owing to the discovery of novel structural and dynamical features that differ from those observed in isolated networks. In the past decade, the mathematical frameworks for characterizing the robustness of a network of networks [27] or multilayer networks [28] have been studied in various settings, such as full interdependency [24], partial interdependency [29], interconnections [30], spatially embedded networks [31], multiple supports [32], directed networks [25], targeted attacks [33], multiple networks [34], and many more. The robustness of multilayer networks has a broad impact on infrastructure networks [35], ecological systems [36], social networks [37], and financial networks [38].…”

“…None of the previously described frameworks can be directly applied to multilayer biological molecular networks. Those approaches are, for the most part, agnostic of their applied setting and deal with networks of the same type, which are either all undirected [27] or all directed [25,50], and in which where the interdependence relations are random. By contrast, biological networks include both directed and undirected network layers, and the non-randomly connected links between layers are of different types.…”

Mitigate Cascading Failures on Networks using a Memetic Algorithm

“…Because these complex networks play an important role in society, their robustness is pivotal234. However, most of these infrastructures have been found to be heterogeneous and to have a power-law degree distribution156.…”