# Resilience Analysis of Traffic Network under Emergencies: A Case Study of Bus Transit Network
## 3 Methodology
### Transport Network Resilience Analysis Model Based on Complex Network  
From the perspective of static resilience in the definition of this article, the basic service function of the bus network is to transport passengers from one station to another. When a sudden event interrupts the connection between two stations, the most effective method is to choose another bus route that connects the two stations. Therefore, the recovery of the transportation function between two stations largely depends on whether there are alternative paths besides the normal path. In short, based on the definition of resilience in this article, if the bus network can provide more shortest paths to reach the destination in the event of a sudden event, then the bus network has a relatively high resilience value. [PERSON] et al. proposed a similar definition of resilience, defining it as the number of reliable routes between any two nodes, to calculate the ability to restore transportation function after partial road closure [51]. From the perspective of complex networks, the resilience of a bus network can be evaluated by the weighted average of centrality indicators of the bus network's stations and routes. Based on this idea, this study abstracts the bus network into a weighted complex network similar to a BA scale-free network. Nodes and edges are important components of complex networks, and analyzing their importance is a key approach to analyzing complex networks. In general, centrality measures such as degree centrality are commonly used to analyze the importance of nodes and edges in a network. Nodes and edges that have a greater impact on the structure and function of the entire network are generally more important. Although these important nodes and edges are relatively few in number, their influence can quickly spread throughout the entire network. Given the need to analyze the resilience of the bus network in this study, identifying the importance of network nodes and edges becomes the first problem to be solved. There are currently many different methods for calculating network node centrality, including degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality. Degree centrality reflects the  
Figure 9: Model verification results. degree of centralization or concentration of the network and is suitable for situations where the entire network operates around a set of core nodes. Betweenness centrality is developed around the concept of betweenness and can measure the information transmission ability of a node or edge. The calculation method for betweenness centrality involves counting the number of times the shortest path passes through a node. Nodes with high betweenness centrality, like transportation hubs, bear a large information transmission task. Closeness centrality reflects the size of the average distance between the selected node and other nodes in the network. The smaller the average distance, the more central the node is in the network. The definition of closeness centrality is the reciprocal of the average length of the shortest path between the node and all other nodes in the network. Based on this, this study proposes a bus network resilience analysis model based on node closeness centrality and edge betweenness centrality, as shown in Figure 10.  
To facilitate the description of the model's calculations, this study introduces the mathematical symbols shown in Table 1: