# Vulnerability Analysis of a Multilayer Logistics Network against Cascading Failure
## 1 Introduction
In logistics networks and even supply chain networks, the vulnerability of cascading failures is common, such as cascading failure modeling for logistics networks based on the local information of nodes [21; 22], cascading failure propagation in logistics systems [23], cascading failure in evenly distributed logistics support networks [24], and importance evaluations of nodes under cascading failures of logistics infrastructure [25]. In addition, the mechanism of vulnerability in a logistics service supply chain was also researched [26; 27]. However, compared to single networks, multilayer network models can better represent real-world systems. With the reshaping of global logistics networks, seaports and airports are engaged in international trade [28]. The interactions among networks have increasingly become intensive and complicated. It is a given that in multilayer global logistics networks, cities of a single layer are interdependent or interconnected to cities in other layers. Examples of multilayer networks can be found in different complex network research. In maritime areas where networks of ports interact with each other, [PERSON] et al. researched the global shipping network as a multilayer structure consisting of three types of freighters [29]. [PERSON] analyzed the interdependence between maritime networks and different commodity flows [30]. [PERSON] further introduced socioeconomic factors to converge the ports to regional administrations [31]. In air cargo networks, where airports are interdependent, [PERSON] regarded the top 15 airlines in Europe as 15 levels, establishing a European aviation network [32]. The organization of a logistics enterprise network is mainly devoted to the analysis and comparison of the degree and connection between cities and is tightly integrated with the construction of urban networks [33]. Alternatively, in an international trade network, [PERSON] et al. introduced indicators such as infrastructure and trade facilitation to construct a trade network and its support network [34]. These studies have suggested that a multilayer network connects different cities on different scales. In fact, a collapsed node in a multilayer network can cause more damage than a single node in a logistics system. Besides, the global and heterogeneous characteristics of networks could have a significant impact on the vulnerability of large systems and strategies to limit the spread of failures [35]. The correlation between heterogeneous logistics networks makes a logistics system more vulnerable while being more powerful and thus facing greater risks. When two or more subnetworks are interdependent, a fraction of city failures in one layer can trigger a cascading failure phenomenon that propagates in a multilayer global logistics network. New aspects of the vulnerability of networks emerge when interdependencies of different layers are considered. In the research on the vulnerability of cascading failures, the highest load or the lowest attack strategy was found. The highest load attack is often directed at nodes with the greatest connectivity or load. This strategy is based on the rationale that by targeting the most critical nodes, the overall network robustness can be significantly diminished [36]. Conversely, the lowest load attack, sometimes overlooked in comparison, targets nodes with the least load. This approach may not immediately impact the network's core functionality but can lead to a gradual degradation of network performance over time [37]. Recent studies have indicated that the effects of these attack strategies on the network are closely related to tunable parameters. For instance, the attack on edges with lower loads can result in larger cascading failures than those with higher loads under certain conditions [38]. Moreover, in the context of interdependent networks, the coupling strength between networks can influence the effectiveness of these attacks.