# Vulnerability Analysis of the China Railway Express Network Under Emergency Scenarios
## 6 Conclusions  
This study quantitatively analyzes the topological feature parameters of the CRN, demonstrating that it is a typical scale-free network. It also establishes a vulnerability network cascade failure model that incorporates the impact of cargo flow. The findings reveal that sudden events causing network node failures result in earlier and more extensive network cascade failures with greater external disturbances. Deliberate attacks based on node strength have a significantly larger impact on the network than those based on node degree and node betweenness. Variations in the topological coupling coefficient and cargo flow coupling coefficient have distinct effects on network vulnerability. As the topological coupling coefficient increases, the node at the highest risk shifts from the strongest to the most highly connected, leading to more severe cascade failures for attacks targeting nodes with the greatest betweenness. Similarly, an increase in the cargo flow coupling coefficient shifts the node at the highest risk from the most highly connected to the strongest, resulting in more severe cascade failures for attacks on nodes with the greatest betweenness. The study also examines the influence of cargo flow allocation methods, finding that adjusting the cargo flow allocation coefficient can delay the time of all node failures when the strongest node is attacked. In the event of an edge failure, the intricate structure of the network renders the effects of intentional attacks on its edges nonlinear and multifaceted. The influence of various edge removals on cascading failures is not only contingent upon their betweenness and weight but also profoundly influenced by their position within the network and their interconnections with other edges. This nuance can be leveraged to judiciously disrupt specific edges during emergencies, thereby mitigating the propagation of cascading failures. In contrast to random faults, the CRN exhibits a heightened vulnerability to intentional attacks, underscoring its scale-free nature. Altering the topological coupling coefficient does not markedly alter the network's susceptibility. However, an increase in the flow coupling coefficient expedites the propagation rate of cascading failures within the network, leading to more profound consequences. When a network edge is targeted by intentional attacks, a single-factor flow allocation approach tends to favor either reducing or increasing the flow coefficient as a means to curtail the spread of cascading failures. In instances where simultaneous failures occur at both nodes and edges, deliberate attacks on influential nodes and edges can expedite the propagation of cascading failures. However, given the high connectivity and redundancy inherent in these networks, the extent of cascading failure propagation is comparatively limited. Even when such attacks eliminate the most critical nodes and edges based on primary network indicators, they may not induce the further propagation of cascading failures due to the inherent stability of the network. This study examines the influence of diverse emergencies on the CRN, as well as the distribution of cargo flow within this network. However, due to the substantial volume of cargo and the container transportation mode employed by the CR express, more intricate distribution routes and methods may be required for cargo flow allocation. Furthermore, consolidation centers already functioning within the CRN serve as crucial transit points. The reliability of these nodes and the distribution of cargo flow are vital to the overall stability of the network. Future research could delve into the specific impact of topological coupling and cargo flow coupling at consolidation centers on the network, particularly in instances where consolidation centers fail, examining the propagation and extent of cascading failures within the network. Conceptualization, L.Z. ([PERSON]) and H.L. ; methodology, L.Z. ([PERSON]); validation, L.Z. ([PERSON]) and P.Y. ; formal analysis, W.Z.