## 4 Case Study
### Simulation Analysis of Accessibility Measurement
It is also notable that railway networks have a certain degree of design redundancy, which offers a certain buffer in the initial stages of the disturbance. In comparison with random disturbance simulations, targeted disturbance simulations such as external attacks and fluctuations in passenger and freight traffic will lead to a rapid decline in the network clustering coefficient. This is because such disturbances tend to remove the most critical nodes within the network. Random disturbances typically change more slowly as the disturbances are randomly distributed throughout the entire network. In the simulations of targeted disturbances like external attacks and fluctuations in passenger and freight traffic, the degree or betweenness is recalculated after each node is removed, which results in the selection of different nodes for removal at different stages, causing the clustering coefficient to change nonlinearly. Edge-based random disturbances initially cause a slower decline in the clustering coefficient because the overall connectivity of the network remains relatively high. As the disturbance proceeds, especially when important connection edges are removed, the clustering coefficient might decline more significantly. (3) Changes in Network Efficiency under Different Railway Network Disturbance Events  
The efficiency of China's railway network in the absence of experiencing disturbance events is 0.16564. Simulations were conducted on the nodes of China's railway network for the four major types of disturbance events, namely external attacks, natural disasters, technical malfunctions, and fluctuations in passenger and cargo traffic. The changing trends of network efficiency under different railway network disturbance events were obtained through simulation, as shown in Figure 7a,b below. It can be discerned from the figure that in the perturbation simulation based on the initial degree and betweenness, the most crucial nodes in the network (i.e., the nodes with the highest degree or betweenness) are removed initially, which typically leads to a sharp drop in network efficiency. As these nodes are eliminated, the network may rapidly disintegrate into smaller disconnected subnetworks, thereby causing a further decline in efficiency. In the perturbation simulation involving the recalculation of degree and  
Figure 6: (**a**) Trend of average agglomeration coefficient of network under natural disaster and technical fault simulation. (**b**) Trend chart of the average agglomeration coefficient of the network under the simulation of external attacks and passenger and cargo flow fluctuations. “Initial Degree” represents “simulation of initial degree perturbation”; “Recomputation Degree” represents “simulation of recomputation degree perturbation”; “Initial Betweenness” represents “simulation of initial betweenness perturbation”; “Recomputation Betweenness” represents “simulation of recomputation betweenness perturbation”. betweenness, the degree and betweenness of the remaining nodes are recalculated after each node is removed. This strategy shifts the focus of the perturbation from the initially highly connected nodes to other, less optimal nodes, resulting in a slower rate of decline in network efficiency or, in some cases, a temporary rebound, particularly when less critical nodes are removed. This enables the remaining network to quickly reorganize and maintain a certain level of efficiency. In random disturbances such as natural disasters and technical glitches, nodes or edges within the network are randomly selected and removed. Since the randomly chosen nodes are not necessarily the critical ones, this perturbation simulation results in the slowest rate of decline in efficiency. Meanwhile, several characteristics can be observed:  
1. The network may self-organize after the removal of nodes or edges to find more efficient paths, which is the cause of the temporary stability or improvement of efficiency. 2. After the removal of certain nodes, the network may fragment into multiple smaller subnetworks.