# A Vulnerability Index for Multimodal Transportation Networks: The Case of Korea
## 4 Results
A higher value from the vulnerability function indicates that the group is more vulnerable within the network. Given the significant variation in the original data values, Z-score normalization was also applied to the vulnerability results for group nodes. Figure 3: Visualization based on single-node vulnerability results. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Region** & **Original Value** & **Z-Score Value** \\ \hline Gyeongggi-do & 9608 & 2.88 \\ Gyeongsangbuk-do & 6538 & 1.56 \\ Jeollanam-do & 3936 & 0.44 \\ Chungcheongnam-do & 3285 & 0.15 \\ Jeollabuk-do & 3264 & 0.15 \\ Gangwon-do & 3098 & 0.07 \\ Seoul & 2914 & 0.00 \\ Chungcheongbuk-do & 2580 & \(-\)0.15 \\ Gyeongsangnam-do & 2252 & \(-\)0.29 \\ Busan & 1477 & \(-\)0.62 \\ Ulsan & 1257 & \(-\)0.72 \\ Daegu & 1248 & \(-\)0.72 \\ Incheon & 1015 & \(-\)0.82 \\ Gwangju & 781 & \(-\)0.92 \\ Daejeon & 628 & \(-\)0.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Group-node vulnerability results (sorted by highest vulnerability). Gyeonggi-do recorded the highest vulnerability score, highlighting its role as the most vulnerable region within Korea's transportation network. As a major transportation hub in the Seoul metropolitan area, Gyeonggi-do maintains strong connections with surrounding nodes and plays a central role in the network. Similarly, Gyeongsangbuk-do recorded the highest score among regional areas, demonstrating its function as a relatively vulnerable hub within the regional transportation network. On the other hand, Daejeon has the lowest vulnerability score of \(-0.99\), indicating stronger connectivity with neighboring regions. This underscores the need for policy efforts to strengthen inter-regional connections and improve resilience. Seoul, with a neutral Z-score of 0.00, maintains network stability not through independent connectivity but through its interactions with Gyeonggi-do and Incheon. However, major regional metropolitan cities in the provinces exhibit relatively low vulnerability, indicating the need for improvements to ensure balanced development in regional transportation networks. Figure 4 visualizes the vulnerability index of group nodes, where darker colors indicate higher network vulnerability. The metropolitan area (Gyeonggi-do and Seoul) serves as the central axis of the network, exhibiting relatively high vulnerability and maintaining network stability. These regions are likely to provide alternative routes even if certain nodes are removed, contributing to the resilience of the network. In contrast, regional metropolitan cities such as Daejeon, Gwangju, and Daegu show lower vulnerability. This suggests a need for policy efforts to strengthen their connectivity with surrounding regions and reduce the likelihood of disconnection from neighboring nodes. These regions face a relatively lower risk of network disruption, emphasizing the importance of enhancing connections and securing alternative routes to ensure network robustness. The results of the group analysis reveal that major regional metropolitan cities in Korea exhibit relatively higher vulnerability, indicating a need for improvements to achieve balanced development within regional transportation networks. These findings emphasize the importance of policies aimed at enhancing inter-regional connectivity and improving  
Figure 4: Visualization by region based on the vulnerability results of group nodes. the overall efficiency of the transportation network. Figure 5 shows that regions with higher centrality generally have lower vulnerability, whereas those with weaker connectivity tend to be more vulnerable. Busan (Star mark) appears structurally central but still exhibits notable vulnerability, implying that centrality alone does not fully explain resilience.