# Vulnerability Analysis of a Multilayer Logistics Network against Cascading Failure
## 1 Introduction
The rise or fall in absolute change is manifested in increases or decreases in connectivity, control, breadth of linkage, and intensity of linkage. b. The relative change of enhancement or decline is manifested in the fact that even if it maintains its original level of centrality or even improves it, it may still be in a state of relative decline along with the increase in the level of centrality of other cities. All of the above changes will affect the influence and power of the logistics hub city to change and alter its position in the logistics network system. The above two connotations constitute the paradigm of a logistics hub city and thus analytically define a logistics hub city: a logistics hub city is a basic node city based on the logistics network connection, realizing the flow and allocation of resource elements, and dynamically exerting influence and power. Vulnerability is one of the fundamental properties of complex systems. Incidents or attacks can cause the collapse of logistics systems, such as natural disasters such as typhoons, targeted attacks such as destruction of the economy and trade, or even overload lines due to poor node capacities. An attack can cause great damage across cities worldwide and their surrounding regions (hinterlands). Taking economic and trade destruction as an example, a trade war between two countries will inevitably be accompanied by a reduction in trade orders and then cause a reduction in logistics demand. In a global logistics network, cities may face the problem of excess capacity and freight rates. In addition, due to a trade war, the market would continue to have a negative impact; thus, cities could even fail, and freight volume could plummet. Moreover, overloading cities may cause other kinds of problems. For instance, in the past 20 years, approximately half of all recyclables in the world have been shipped to China. However, beginning in July 2017, China announced that it would no longer accept 24 kinds of solid waste imported from other countries. As a result, large amounts of solid waste were transferred to other countries. Vietnam has already handled thousands of foreign containers containing solid waste, resulting in a shortage of support at Cat Lai. That shortage has caused more than 1000 containers to remain in the port of Cai Mep, adversely impacting port operations. Therefore, Vietnam decided to suspend the import of waste plastics and restrict the import of waste paper. As a result, Thailand, Malaysia, and Indonesia may be overloaded due to the large volume of waste imported from China. The impacts of this event have been amplified due to the interdependencies of cities, which are causing cascading failures. Cascading failures are common and have recently received much attention. Localized failures or attacks on nodes can cause cascading failures and ultimately lead to the breakdown of a whole network, as widely researched in different types of networks [1]. This includes model descriptions [2; 3; 4], strategies for control or defense [5], and scenarios in real networks such as power grids [6; 7; 8], transportation infrastructure [9; 10], and social networks [11; 12]. In addition, the model was extended considering flows in interconnected networks or interdependent networks [13; 14]. Furthermore, the definition of vulnerability may vary in different research areas. In general, vulnerability is defined as a property that makes the structure and function of a system susceptible to changes due to its sensitivity to disturbances. In this paper, vulnerability is measured by the decrease in efficiency from its original state after the disruption. A network is considered vulnerable if it changes sharply and suffers large cascading failures due to its properties. For strategies, attacks on nodes and edges have been widely used. Specifically, nodes or edges can be removed by the rank of degree [15], betweenness [16], eigenvector [17], PageRank [18], link [19], or path [20].