# Vulnerability Analysis of a Multilayer Logistics Network against Cascading Failure
## 1 Introduction
When the coupling strength is weaker, attacking edges with a lower load can be more detrimental than attacking nodes with a higher load. However, this relationship reverses when the coupling strength is stronger [39]. The research also highlights the importance of local load redistribution in assessing network vulnerability. For example, in the US power grid, a reduction in the initial load can affect the critical threshold of the tolerance parameter differently depending on whether the attack is on the highest load nodes or the lowest load nodes. This finding underscores the need for a nuanced understanding of attack strategies and their potential impact on network performance [40]. As discussed above, the vulnerability of cascading failures is an important and active research field of multilayer networks that shows different structural characteristics and practical implications compared to single networks. However, the increasing research on vulnerability brings new questions. A major challenge is the design of a multilayer network to converge different logistics sublayers using the interdependencies of cities, such as the degree of overlap among the different layers of circulation composing global maritime flow [41]. However, most research is still limited to the assumption that one network does not have any connection with another network. Maritime transport, air transport, business organization, and international trade all have important respective roles in the development of cities, and sometimes the four are complementary. As long as network layers are constructed due to logistics hub city node connections, any changes observed between the topologies of the different layers illustrate the impact of network layer dependencies on node connections. Because attacks are rarely limited to a single layer in reality, the other question concerns the mechanism of cascading failures on the overloaded node of multilayer networks and how far the overload will affect the surrounding nodes. In particular, most articles have focused on modeling, and few of them are networks in the real world. In these models, the initial load is determined by the degrees and a parameter [42; 43; 44]. Their results could be more convincing if they simulate the load in the real world. Therefore, this paper aims to fill part of this important research gap by converging different single networks, including a maritime network, air cargo network, logistics enterprise organization network, and international trade network. In addition, a load redistribution algorithm is introduced, where a weighted degree is used as the initial load, and a capacity parameter is used as the capacity of the load. Using the normalized metric of efficiency, the different attack scenarios include attacking the most important node and the least important node. As mentioned above, the subnetwork and even the converged network are compared. Furthermore, the primary contribution of the study is not only to extend classic notions to analyze the vulnerability of a multilayer network but also to make it possible to capture the properties of real multilayer logistics networks. The rest of this paper is organized as follows. In Section 2, the model and data applied to the global logistics network are briefly described. It also describes attack strategies,especially cascading failures, using a load algorithm. The topological metrics are also contained. In Section 3, the topological properties of the global logistics network, such as being scale-free and small world, are described. In Section 4, a vulnerability analysis presents the results for the single-layer networks and the multilayer network. It also discusses the implications of these results for vulnerability in the global logistics network. Finally, the summaries and conclusions are shown in Section 5.