## 4 Case Study
### Simulation Analysis of Accessibility Measurement  
Based on the computational process outlined in the preceding text, MATLAB was utilized to simulate the variations in resilient accessibility metrics under different disturbance events in the railway network. (1) Changes in the pairs of reachable nodes under various railway network disturbance events  
In the initial state, any two nodes in the Chinese railway network were mutually accessible, and no isolated nodes existed. However, as disturbance events occurred, the number of reachable node pairs in the network gradually decreased. By simulating the four major types of disturbance events--external attacks, natural disasters, technical malfunctions, and fluctuations in passenger and cargo traffic--on the railway network nodes in China, the changing trends of reachable node pairs under different disturbance events were obtained through simulation. These trends are presented in Figure 5a,b. The figure clearly illustrates the changing trend in the number of reachable node pairs in the network under different disturbance events. Under such random disturbances as natural disasters and technical malfunctions, the rate of decrease in the number of pairs of reachable nodes resulting from edge-based random disturbances is relatively slow. In contrast, when disturbance simulation with recalculated betweenness is adopted, the rate of decrease in the number of pairs of reachable nodes is the fastest. This suggests that disturbances like natural disasters and technical failures, due to their nonspecific nature, do not cause network degradation as quickly as other disturbance strategies. Compared to the initial disturbance strategy, the recalculated disturbance strategy has a more pronounced effect on the number of pairs of reachable nodes in the network, and the change is also more rapid. (2) Changes in the clustering coefficient under different railway network disturbance events  
The initial average clustering coefficient of the railway network in China is 0.10199, indicating a relatively low degree of network aggregation and a sparse structure. By separately simulating the four major types of disturbance events--external attacks, natural disasters, technical failures, and fluctuations in passenger and cargo traffic--on the nodes of the railway network, the changing trends of the clustering coefficient under different railway network disturbance events obtained through simulation are shown as follows in Figure 6a,b. As can be observed from the figure, the overall variation in the clustering coefficient gradually diminishes as the disturbance event progresses. Concurrently, as nodes or edges are removed, the size of the network gradually decreases. Once the number of nodes decreases to a certain extent, the average clustering coefficient might fluctuate, particularly when the network splits into multiple disconnected subgraphs. Additionally, when the network is partitioned into smaller, closely connected groups, the clustering coefficient might temporarily increase since more triangular relationships can form within the groups. That is, as nodes or edges are continuously removed, smaller subgraphs with higher  
Figure 5: (**a**) Trend diagram of reachable node pairs under natural disaster and technical fault simulation. (**b**) Trend chart of reachable node pairs under external attack and passenger and cargo flow fluctuation simulation. (**a**) Based on Nodes” represents “simulation of random perturbation based on nodes”; “Based on Edge” represents “simulation of random perturbation based on edge”; “Initial Degree” represents “based on initial degree-based attack”; “Recomputation Degree” represents “degree recomputation-based attacks”; “Initial Betweenness” represents “based on initial betweenness centrality-based attack”; “Recomputation Betweenness” represents “recomputation-based betweenness centrality attack”. clustering coefficients may emerge, leading to an increase in the clustering coefficient at certain stages.