# A Vulnerability Index for Multimodal Transportation Networks: The Case of Korea
## 4 Results  
Figure 2 illustrates the network graph constructed using the KTDB network and OD data. The Korea Transport Database (KTDB) is a comprehensive database that provides information related to the national transportation network in South Korea, including data on various modes of transportation such as roads and railways. The network graph consists of a total of 48,067 nodes connected by directed links. Each node and link are designed to represent the directional nature of the network. The visualized network graph highlights the concentration of major nodes in the metropolitan area, emphasizing its role as a hub within Korea's transportation network, where traffic demand and supply are heavily centralized. 1. Vulnerability of Individual Nodes We defined the vulnerability of individual nodes within the network as the extent to which they are connected to or isolated from the rest of the network, and we quantified this measure accordingly. The calculation of individual node vulnerabilities revealed significant variation in the original dataset values across nodes. To ensure objectivity and enable meaningful comparisons, Z-score normalization was applied. This normalization standardized the data to a mean of 0 and a standard deviation of 1, allowing for a clear and consistent comparison of the relative vulnerability of each node. Nodes with low vulnerability scores indicate that they are relatively less vulnerable due to their stronger connectivity with neighboring nodes. The analysis reveals that these nodes are often located slightly outside the core areas of Korea's transportation network. Notably, node 345121, which exhibits a high vulnerability score, is situated in Pyeongchang, Gangwon-do. Conversely, nodes with high vulnerability scores are predominantly located in key connection points in peripheral regions, such as Wonju City in Gangwon-do and Pohang in Gyeongsang bulk-do, outside the Seoul metropolitan area (see Table 4). Figure 3 visualizes the vulnerability index of individual nodes based on their Z-scores, where darker colors indicate lower network vulnerability. The analysis of Korea's transportation network vulnerability reveals that nodes in the metropolitan area exhibit the lowest vulnerability, indicating that the metropolitan region holds a structurally stable position within the network. In contrast, some nodes in other regions show high vulnerability, revealing disparities across the network. These results highlight the structural characteristics and regional differences within the transportation network. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Node** & **Region** & \begin{tabular}{c} **Original** \\ **Value** \\ \end{tabular} & \begin{tabular}{c} **Z-Score** \\ **Value** \\ \end{tabular} & \
\begin{tabular}{c} **X-** \\ **Coordinate** \\ \end{tabular} &
\begin{tabular}{c} **Y-** \\ **Coordinate** \\ \end{tabular} \\ \hline
59 & Gyeonggi-do & 0 & 1.29 & 127.7212 & 37.53116 \\
14 & Gangwon-do & \(-1\) & 0.20 & 128.1868 & 37.54866 \\
1 & Gangwon-do & \(-2\) & \(-0.88\) & 128.2442 & 37.57988 \\
2 & Gangwon-do & \(-3\) & \(-1.97\) & 128.2699 & 37.55557 \\
30 & Busan & \(-4\) & \(-3.06\) & 130.2406 & 35.11808 \\
204 & Gyeongangbuk-do & \(-5\) & \(-4.14\) & 130.4723 & 35.84891 \\
187807 & Gyeonggi-do & \(-6\) & \(-5.23\) & 127.9714 & 37.45731 \\
180392 & Gyeonggi-do & \(-7\) & \(-6.32\) & 127.7347 & 37.44321 \\
345121 & Gangwon-do & \(-8\) & \(-7.40\) & 128.2956 & 37.6338 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Single-node vulnerability results summary (in order of low vulnerability). Figure 2: Korea’s traffic network graph results. In summary, peripheral areas outside the metropolitan region are key to maintaining network stability and improving regional connectivity. These nodes should be prioritized in efforts to enhance transportation network resilience and inter-regional connections. 2. Vulnerability of Group Nodes  
We derived the vulnerability of group nodes within the network using a vulnerability function (see Table 5).