# Vulnerability Analysis of the China Railway Express Network Under Emergency Scenarios
## 1 Introduction  
As the \"Belt and Road\" initiative continues to deepen, the China Railway Express (CR Express) has emerged as a crucial conduit for fostering pragmatic cooperation among Eurasian nations. This initiative carries the historical responsibility of promoting economic and trade development along the Silk Road Economic Belt. The CR Express, relying on the Siberian Continental Bridge and the New Eurasian Land Bridge, has established three transportation corridors, western, central, and eastern, linking countries along the Silk Road. In recent years, cities across China have actively launched CR Express services, driving the nation's reform and opening-up policies from east to west, and gradually expanding from coastal to inland areas. This has led to a new pattern of land-sea domestic and foreign linkages, characterized by east-west mutual assistance and comprehensiveopenness. In 2020, the annual number of CR Express services surpassed 10,000 for the first time, and, by 2023, the total reached 17,523. Over the past decade, the CR Express has opened a new land transportation corridor between Asia and Europe, reaching 217 cities in 25 European countries and regions, as well as over 100 cities in 11 Asian countries and regions along its routes. The CR Express is gradually forming a network layout characterized by a combination of main and feeder lines and hub-based distribution. Although this structure operates with high efficiency, it has poor risk resistance and stringent operational demands. Key railway ports, such as Alashankou, Erenhot, and Malaszewicz, serve as vital transit points for most trains, making them critical nodes that can dictate the operational state of the entire network. When issues arise at these stations, the network's performance is significantly affected. For example, in the latter half of 2021, the renovation of the Malaszewicz station led to the closure of half of the channels, resulting in increased delays and reduced overall transport efficiency. Additionally, during the COVID-19 pandemic, the China-Kazakhstan border faced increased customs procedures and a decreased transportation capacity, which diminished the timeliness advantage of the CR Express. Regional stability, unforeseen events, and political factors also impact CR Express operations. Events such as the 2021 German railway strike, Kazakhstan's political unrest in 2022, and the Russia-Ukraine conflict in 2022 led to train delays and increased freight costs. Besides station-specific issues, force majeure events such as extreme wind conditions at the China-Kazakhstan border, floods in Turpan and Xinjiang, and heavy rainstorms in Zhengzhou also disrupt CR Express operations, causing delays in both outbound and return trips. Therefore, it is essential that we analyze the CRN to identify its strengths and weaknesses and to propose improvement measures that can mitigate adverse events and risk factors. Studying the vulnerability of the CRN under emergencies and identifying weak links in the network is crucial for ensuring stable train operations and the safety of goods. The existing research suggests that the CRN exhibits power-law distribution characteristics, primarily caused by preferential attachment mechanisms. When nodes in the network are attacked, increasing the flexibility of transfer methods can enhance the network's dynamic resilience, thereby improving its ability to suppress cascading risk propagation. This highlights the close relationship between network structural features and dynamic response mechanisms in the face of attacks. Current studies have also explored the interactions between traffic flow, risk, and cascading failures within the binary supply-demand relationship of transportation stations in the CRN, introducing the concept of the \"ripple effect\" [1; 2]. These studies provide valuable insights into understanding the performance of the CRN under risk.