Abstract
Cascading failures between interdependent multilayer networks are being widely studied, especially the trend of robustness caused by the interlinks between networks. However, few researchers pay attention to the effect of the interlink topology on the robustness of coupled networks, which is a critical interlink factor of multilayer networks. In this study, the method frame of multilayer network experiment simulation is given. Through numerical simulation and actual network simulation, the exhaustive method is used to enumerate all the patterns of interlink topological relations of multilayer networks (three-layer or more). The research verifies that the interlink topology affects the global robustness and that there exists a fragile interlink pattern in the patterns of interlink topologies. The star-like interlink pattern with the most uneven interlink-degree distribution leads to the weakest robustness; the pattern with average interlink-degree distribution reveals good global stability as a loop-like pattern or entire interlink pattern. In addition, the influence of interlink topology is independent. The simulation results are not affected by the network layer number and intraparameters (including the network-generated form, each layer of network node number, and average degree of each layer of network). Thus, ignoring the interlink topology may result in the actual system suddenly becoming vulnerable before the theoretical calculation point. Interlink topology as an independent factor affecting the robustness of multilayer networks should be paid more attention.
Highlights
The majority of real networks are not isolated but exist in an interconnected complex network
Buldyrev et al [4,5,6] established a research framework based on the percolation theory and described the functional formalization as a two-layer coupled network, which described the robustness of the phase transition
The percolation theory highlights the static changes in the network topology under external effects, which is suitable for evaluating the influence of topology changes between layers on system robustness
Summary
The majority of real networks are not isolated but exist in an interconnected complex network. The synthetic interactions between interdependent networks make the networks fragile because of the failures that occur in one system and spread to other systems [1,2]. In emergencies such as natural disasters or deliberate attacks, the failure of a single network may result in the failure of the functions of other networks associated with it, and the failure of multiple networks successively occurs, which is known as cascading failure. Robustness indices are often used to capture cascading failures. If cascading failures can occur in the coupled network, the system is said to be fragile; that is, the robustness of the system is poor. A first-order phase transition (discontinuous phase transition) was observed, which was significantly different from the second-order phase transition (continuous phase transition) observed in isolated networks
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