# Resilience Analysis of Traffic Network under Emergencies: A Case Study of Bus Transit Network
## 4 Case Analysis
### Experimental Process and Result
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Bus Stop** & \(\theta\) & \(\lambda\) & \(\rho\) & \(\tau\) & \(\sigma\) & \(R_{I}\) \\ \hline Sihui Hub Station & 0.5125 & 0.2189 & 0.8101 & 0.5552 & 0.3911 & 0.3752 \\ Bawangfen West Station & 0.4344 & 0.6237 & 0.9912 & 0.6792 & 0.4463 & 0.5178 \\ Langjiayuan Station & 0.3124 & 0.2935 & 0.8646 & 0.7919 & 0.3048 & 0.1953 \\ Dabeiyao West Station & 0.5213 & 0.6892 & 0.6774 & 0.5481 & 0.4685 & 0.4063 \\ Yong’anli Intersection West Station & 0.7525 & 0.3487 & 0.9344 & 0.5598 & 0.2839 & 0.6474 \\ Ritan Road Station & 0.4687 & 0.65 & 0.8789 & 0.7931 & 0.2486 & 0.3915 \\ Yabao Road Station & 0.5173 & 0.4885 & 0.6564 & 0.6884 & 0.3299 & 0.2985 \\ Chaoyangmeni Station & 0.458 & 0.5502 & 1.0466 & 0.4297 & 0.4176 & 0.6281 \\ Chaonei Xiaojie Station & 0.6182 & 0.8047 & 1.1535 & 0.7485 & 0.4337 & 0.9516 \\ Dongiskou East Station & 0.251 & 0.2625 & 1.3992 & 0.6247 & 0.3671 & 0.3666 \\ Art Museum East Station & 0.3462 & 0.353 & 0.8743 & 0.6163 & 0.2468 & 0.2490 \\ Beach Crossing West Station & 0.6369 & 0.4892 & 0.891 & 0.2988 & 0.3981 & 0.7217 \\ Palace Museum Station & 0.3748 & 0.2293 & 0.8367 & 0.7438 & 0.2956 & 0.2162 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Resilience factors and total resilience of 13 stops. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Line** & \(\theta\) & \(\lambda\) & \(\rho\) & \(\tau\) & \(\sigma\) & \(R_{I}\) \\ \hline
1 & 0.6127 & 0.0792 & 0.8913 & 0.6238 & 0.3261 & 0.3952 \\
139 & 0.6791 & 0.4331 & 0.7896 & 0.7139 & 0.3968 & 0.5057 \\
101 & 0.5292 & 0.0852 & 1.1572 & 0.7029 & 0.4519 & 0.5216 \\
116 & 0.6154 & 0.0841 & 1.1229 & 0.7316 & 0.3742 & 0.5083 \\
27 & 0.4687 & 0.1127 & 0.8446 & 0.638 & 0.4929 & 0.3507 \\
40 & 0.5983 & 0.1481 & 1.1795 & 0.7179 & 0.3484 & 0.5547 \\
60 & 0.4894 & 0.0936 & 0.7022 & 0.4313 & 0.4204 & 0.3143 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Resilience factors and total resilience of 7 lines. (3)Bus network resilience analysis  
First, the data of 152 bus routes and 1547 bus stations are abstracted into a topology graph using the NetworkX tool package in Python. The result is shown in Figure 19.  
Figure 19: Topological structure and degree distribution of public transit network. Figure 18: Smooth data comparison. From the degree distribution in Figure 19, it can be observed that the bus network exhibits a scale-free property, where the degree values follow a power law distribution. This means that a small number of nodes have relatively high degrees, while the majority of nodes have lower degrees. This observation aligns with the natural distribution of bus network stations, as there are typically only a few major transportation hubs. Such networks are often referred to as heterogeneous networks. The partial statistical characteristics of the bus network in this study are shown in Table 11.  
From the statistical features, it can be observed that the network has relatively low local and global efficiency, indicating that the network has limited global transmission capacity and resilience against small-scale failures. The clustering coefficient is a measure of the degree of clustering among nodes in a network, calculated as the ratio of the number of edges between a node's neighbors to the maximum possible number of edges between these neighbors. The network's average clustering coefficient is obtained by averaging the clustering coefficients of all nodes in the network, reflecting the network's clustering tendency. From the average clustering coefficient of the network, it can be inferred that the network has a relatively low level of clustering. Figure 20 presents four centrality measures for the public transportation network consisting of 152 bus routes. It can be observed that the node closeness centrality and edge betweenness centrality are relatively concentrated, indicating that centrality measures can effectively capture the network's importance.