# Vulnerability Analysis of the China Railway Express Network Under Emergency Scenarios
## 5 Vulnerability Analysis of CRN Under Emergency
### CRN Node Failures
#### 5.1.2 Deliberate Attacks  
In the case of deliberate attacks, this section conducts targeted attacks on the top ten main sites based on three indicators, node degree, node strength, and node betweenness, according to network characteristics. It can be concluded that there is a small-scale cascading failure in the network when external disturbance \(R=1.0\) occurs during random faults. Based on the previous analysis of the characteristics of CR express services, it is known that these services have a strong vulnerability to deliberate attacks. Therefore, the size of external interference is set to 1.0 to analyze the impact of nodes ranked high under different indicators of deliberate attacks on the network.  
The CR Express is a freight network. As shown in the Figure 6, when attacking nodes with high node strength rankings, many nodes cause relatively severe cascading failures to the network. However, when deliberately attacking nodes with high degree rankings, only three nodes cause cascading failures when attacked. When attacking nodes with high betweenness rankings, only two nodes cause cascading failures to the network. This indicates that, in the CRN node strength, i.e., the amount of cargo carried by the node, is a more important factor. This also verifies the characteristic of the CRN as a freight network.  
As can be seen from Table 1, in the ranking of node degrees, cities with the same degree have differences in node strength and node betweenness. Therefore, we selected the cities Zhengzhou and Nanjing, which have different node strengths when their degrees are the same, and the cities Wuhan and Hefei, which have different node betweennesses when their degrees are the same for comparative analysis. The results are shown in Figure 7. It can be observed that, among the cities Wuhan and Hefei, both having a degree equal to 6, Wuhan has a smaller node betweenness. Meanwhile, among the cities Zhengzhou and Nanjing, both having a degree equal to 5, Zhengzhou has a larger node strength. This leads to the conclusion that, in the CRN, the importance of node strength is greater than that of node degree, and the importance of node degree is greater than that of node betweenness.  
Figure 5: Cascaded failure propagation process of CRN point failure under random failure.  
To better reflect the importance of the three node indicators in the network, Xi'an, Wuhan, and Taiyuan were selected as the cities with the top-ranked indicators for intentional attacks. By increasing the external disturbance value, we observed the propagation phenomenon of cascading failures in the network when the external disturbance was increased. As shown in Figure 8, it can be seen that, when the external disturbance was increased, the scale of network cascading failure caused by Wuhan and Taiyuan among the three cities under intentional attack increased. However, as the external disturbance increased, Xi'an accelerated the propagation of cascading failures in the network. Although the increase in external disturbance accelerated the propagation of cascading failures in all three main cities under intentional attack, it can be seen that, when Xi'an was intentionally  
Figure 6: Cascading failure propagation process in networks with deliberate attacks on nodes: (**a**) deliberate attack based on node strength; (**b**) deliberate attacks based on node degree; and (**c**) deliberate attack based on node betweenness.  
attacked, the speed of cascading failure propagation was much greater than when the other two main cities under intentional attack were targeted.