## 2 Related Work
### Design of the Algorithm for Measuring Railway Network Resilience
This restoration strategy entails sorting all the failed nodes based on their degrees or betweenness values and then restoring them one by one in that sequence. Each restored node will maintain its connection pattern in the original network unaltered. The degree/betweenness-based restoration strategy is designed to facilitate the rapid recovery of the network's core structure and functionality, as high-degree nodes are often connected to a large number of other nodes, while high-betweenness nodes serve as pivotal connectors along the shortest paths in the network. By restoring these nodes, the connectivity and overall communication efficiency of the network can be effectively enhanced. Especially after large-scale network disruptions, this strategy can effectively expedite the network's recovery to the normal operational state. By combining network restoration strategies, a simulation algorithm for the restorability of the service network can be devised. The specific implementation steps encompass the following:  
Step 1. Firstly, import the adjacency matrix A of the service network model into MATLAB. Then, determine the total number of nodes N in the network and extract the corresponding node indices. Step 2. Next, the betweenness centrality and degree of each node in the network are calculated and sorted in descending order to generate the network degree list _list_(_ki_) and the network betweenness list _list_[_B_(_i_)]. Following this, a representative perturbation scenario is selected to simulate the impact of network disruptions within the railway system. Step 3. In simulating perturbation events within the railway network, the identification of failed nodes is a critical step. Empirical studies suggest that when the proportion of failed nodes remains between one-fifth and one-fourth of the total number of nodes, the network can typically continue to operate normally. Accordingly, for the purposes of resilience analysis, the number of failed nodes is preset to 100. After simulating a specific perturbation event, specific nodes will be removed from the network based on the pre-selected strategy and then restored. Under a random perturbation strategy, all nodes have an equal probability of being selected for removal. In contrast, for targeted strategies based on degree or betweenness centrality, the top 200 nodes in the degree list _list(ki)_ and the betweenness list _list_[\(B(i)\)] will be removed. Step 4. Following the selection of a recovery strategy, the nodes that failed during the simulated railway network perturbation events are restored sequentially. This process is similar to the previous step of simulating the removal of nodes. Given that different recovery strategies result in varying restoration sequences--and that, in real-world scenarios, limited resources often preclude the simultaneous repair of all failed nodes--the recovery process must proceed incrementally over time. In this algorithmic process, the number of restored nodes is used as a surrogate for time t, meaning that the efficiency of the network is recalculated each time a node is restored. This approach enables the simulation and evaluation of the network's progressive return to normal operational status under specific recovery strategies.