# A Vulnerability Index for Multimodal Transportation Networks: The Case of Korea
## 1 Introduction  
In the evolving transportation systems, we aim to identify vulnerable points in the network and develop quantitative vulnerability indicators to address inter-regional connectivity issues. Modern transportation networks tend to become increasingly complex and demand driven due to socioeconomic activities [1, 2, 3, 4, 5]. These networks directly influence the flow of transportation and logistics systems, acting as crucial factors in either strengthening or weakening inter-regional connectivity [6, 7].  
In South Korea, rapid industrial development is creating increasingly complex multimodal transportation networks, while imbalanced development is leading to the disconnection of certain areas, thereby exacerbating regional disparities. [PERSON] pointed out that the speed, reliability, and ubiquity of transportation networks are critical to societal development, favoring well-connected areas while marginalizing others [8]. Similarly, [PERSON] argued that transportation infrastructure strengthens connectivity between regions and stimulates economic activity [9]. [PERSON] and [PERSON] contend that transportation plays a critical role in enhancing regional productivity and the efficiency of private capital [10]. [PERSON] and [PERSON] also highlighted that transportation networks directly influence regional development through vulnerability, noting that the presence of weak points candiminish accessibility and hinder economic progress [11]. Consequently, as the disparity between regions with well-developed transportation networks and those with insufficient connectivity continues to grow, it is essential to identify vulnerable points and promote equitable development.  
We describe transportation networks from a socio-political perspective, using centralized power structures as an analogy. Centralized control weakens connections among members and, similarly, regions with concentrated transportation flows weaken connectivity to other areas, making surrounding regions dependent and vulnerable. The identification of vulnerable points facilitates the assessment of limitations in mobility and diminished access to economic opportunities and social resources.  
Focusing on Korea's complex multimodal transportation network, we identify and quantify vulnerable nodes by integrating rail and road systems. The proposed vulnerability index analyzes the structural weaknesses of transportation networks, addressing regional imbalances. The results provide a foundational framework for efficient network design and policy decision making. By assessing network vulnerabilities, this research aims to propose strategic and sustainable transportation policies and infrastructure development strategies, offering new directions for efficient and balanced growth.  
We utilize node and edge data provided by Korea's National Transport Database (KTDB). The raw node-edge data and OD matrix data, supplied in TXT format, are modeled and implemented in EMME4. Using the EMME package, we complete the calibration process and convert the results into output files for preprocessing. By processing this data in a Python environment, we construct a transportation network graph and apply graph theory to define vulnerability. Specifically, the analysis focuses on evaluating (1) individual node vulnerability and (2) group node vulnerability. This research adopts a novel approach by leveraging graph theory to assess inter-node connectivity and quantify vulnerability through mathematical functions, moving beyond conventional methods that often focus on localized network characteristics.