A Vulnerability Index for Multimodal Transportation Networks: The Case of Korea

Abstract

This study aimed to assess the vulnerability of transportation networks and identify critical nodes and regions within a multimodal transportation system. While previous research has predominantly focused on centrality measures to evaluate node importance from an accessibility perspective, this study emphasizes the need to evaluate network vulnerability comprehensively in response to rapid socioeconomic changes. We propose a vulnerability function that integrates network topology and connectivity. First, we defined the vulnerability of individual nodes and regional clusters. Second, we developed a methodology to evaluate the defined vulnerabilities systematically. Finally, we applied the framework to Korea’s multimodal transportation network, conducting a case study to validate the effectiveness and applicability of the proposed function. Conclusively, this study presents a comprehensive vulnerability assessment framework for multimodal transportation networks, offering valuable insights to support robust decision making for enhancing sustainable and efficient transportation systems.

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. Dugonjić 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, Hoyle argued that transportation infrastructure strengthens connectivity between regions and stimulates economic activity [9]. Rietveld and Nijkamp contend that transportation plays a critical role in enhancing regional productivity and the efficiency of private capital [10]. Taylor and D’Este also highlighted that transportation networks directly influence regional development through vulnerability, noting that the presence of weak points can diminish 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.

2. Literature Review

Vulnerability analysis has been extensively studied across various fields, including transportation, security, communication, and industrial systems. Initial studies focused on defining vulnerability in a broader context. Cutter (1996) described vulnerability as a measure reflecting the negative impacts of environmental hazards on specific systems, regions, or societies [12]. Delor and Hubert (2000) defined vulnerability as a dynamic process occurring and changing within specific contexts rather than a fixed state [13]. Adger et al. (2006) interpreted vulnerability in the context of socio-environmental systems, defining it as a function of exposure, sensitivity, and adaptive capacity to environmental changes [14]. They argued that understanding vulnerability requires considering not only the likelihood of harm but also the structural and functional limitations of systems. According to their study, vulnerability comprises exposure, adaptive capacity, and protective and defensive factors, shaped by both individual and socio-structural elements. In particular, they emphasized that unequal resource distribution and power dynamics often exacerbate vulnerability [14]. This study advocated for a multidimensional approach, encompassing physical exposure, social sensitivity, and resilience across geographic, social, economic, and environmental dimensions.

In transportation networks, vulnerability analysis has primarily focused on changes in mobility patterns, connectivity, efficiency, and accessibility [15,16,17,18,19]. Holme et al. (2002) defined vulnerability as changes in network performance under various disruption scenarios and analyzed attack vulnerabilities in complex networks, studying the impacts of removing specific nodes or links on structural stability and connectivity [20]. Nicholson and Dalziell (2003) examined how disruptions at specific points influence social, economic, and physical systems, analyzing the relationship between reliability and vulnerability using New Zealand’s regional road network as a case study [21]. In addition, negotiation-based strategies for fair and efficient distribution of energy resources within complex multi-agent systems are becoming important. Ding et al. (2025) established wind, hydrogen, and building energy systems as one integrated multi-agent system (MAES) and proposed a rational resource and profit distribution model that reflects each agent’s contribution through an asymmetric Nash bargaining method [22]. Combined with distributed ADMM algorithms with guaranteed information security, it is argued that it allocates differentiated revenue according to the contribution of each subject and strengthens the collaborative relationship.

Research addressing network vulnerability using accessibility measures has spanned domains like security, tourism, and transportation. Ritchey and Ammann (2000) applied formal techniques in security networks, employing model checking to explore network state spaces and identify potential vulnerabilities [23]. Liu and Man (2005) modeled probabilistic relationships between network states and security threats using Bayesian networks, quantifying the impacts of vulnerabilities on network performance [24]. Jenelius et al. (2006) introduced a methodology for analyzing vulnerable points in road networks, utilizing the concepts of node and link importance to evaluate the impacts of disruptions on travel time and costs [25]. Their approach quantified the significance of specific links and nodes by assessing their influence on accessibility and connectivity within the network [25]. Building on this foundation, Jenelius (2009) further examined Sweden’s road network, assessing the impact of structural characteristics and travel redistribution under disruptions while emphasizing connectivity reinforcement and route diversification as key strategies [26]. Expanding on these findings, Jenelius and Mattsson (2012) proposed a grid-based approach for analyzing regional factors of disruption in road networks, evaluating the impacts of localized node and link failures on network performance [27]. Further, Mattsson and Jenelius (2015) analyzed vulnerability by evaluating functional degradation and the role of critical nodes and links, using accessibility loss and travel cost increases as key indicators [28]. In recent studies, measures to improve network resilience through linkage of transportation and power systems have been proposed. Li et al. (2025) determined that this interaction is a major factor in improving the resilience of transportation networks through an asynchronous distributed restoration framework linking heat demand control of buildings and rerouting of electric buses (E-Buses) [29]. Bell et al. (2008) employed an attacker-defender model to analyze road network vulnerabilities, modeling interactions between intentional attacks and defense strategies to assess both vulnerability and resilience [30]. Taylor (2017) defined vulnerability as the loss of mobility and accessibility due to network disruptions, emphasizing structural and functional analysis through simulations and mathematical modeling [31].

More recent studies have employed graph theory to mathematically model structural vulnerabilities. Phillips and Swiler (1998) introduced a graph-based system for analyzing network vulnerabilities, presenting a methodology to systematically identify structural weaknesses in network security [32]. Their study analyzed vulnerabilities based on the relationships between nodes and edges, with a particular focus on path-based analysis to identify exploitable routes, thereby pinpointing specific security weaknesses in the system [32]. Ammann et al. (2002) proposed a scalable graph-theoretic approach for analyzing network vulnerabilities, emphasizing the importance of mathematically modeling node-link relationships to effectively identify critical points and potential weaknesses within increasingly complex networks [33]. Bozzo et al. (2015) explored the concepts of vulnerability and power in networks, analyzing how node and link interactions affect overall network efficiency and stability. They proposed a methodological framework to evaluate the structural characteristics of networks and the relative importance of individual nodes. Their study concluded that highly influential nodes tend to be more vulnerable [34]. Latora and Marchio (2002) introduced a percolation-based approach, emphasizing the role of giant components and the network’s tolerance to random and targeted node removals [35]. Similarly, Bellingeri et al. (2018) quantified network efficiency loss under different attack strategies, highlighting how connectivity deteriorates through simulation-based disruptions [36]. Innovative approaches leveraging graph neural networks have also been proposed [37,38,39]. While such metrics are useful in modeling dynamic failure scenarios, they typically require extensive simulation and focus on functional performance under hypothetical conditions. In contrast, the vulnerability metric used in this study focuses on structural imbalance within the existing network topology. This approach enables intuitive identification of weakly connected regions without the need for disruption-based modeling, making it particularly suitable for pre-existing, multimodal transportation systems. Despite the growing adoption of graph neural networks, this study adopts a graph-theoretic methodology to ensure objective and precise analysis of transportation network vulnerabilities. This approach mathematically models structural characteristics to effectively identify vulnerable points, ultimately offering actionable insights to enhance system resilience and security.

3. Methodology

We propose a graph theory-based vulnerability scoring indicator for analyzing the vulnerability of Korea’s transportation network. A methodology is proposed for developing vulnerability indices for the Korean transportation network through the following steps: data construction, network and OD matrix configuration, classification of independent and group nodes, identification of neighboring nodes, definition of vulnerability functions, derivation of vulnerability index values for nodes, and a vulnerability index result based on graph theory (Figure 1).

3.1. Data Construction

The transportation network was constructed using the 2019 Korea Transport Database (KTDB), including nodes with geographic coordinates and line data indicating connections and lengths. Network pre-processing and OD matrix integration were performed in EMME4. Centroid connectors were assigned a uniform length of 0.01 km, and intermodal interactions (e.g., transfers between rail and road) were not explicitly represented in the network graph.

In other words, the network reflects a topological structure based on physical connectivity but does not account for modal transfer behaviors or temporal dynamics that may exist in real-world multimodal travel. These assumptions influence the interpretation of structural connectivity in multimodal contexts.

We utilized network and OD (Origin-Destination) data provided by the Korea Transport Database (KTDB). The OD data are provided in matrix format as TXT files, and the network data are structured as IN files, containing node and edge information. The data were processed in EMME4 to complete the assignment stage, constructing a comprehensive network. The constructed network was then exported as a CSV file and rebuilt in a Python environment to facilitate efficient network graph generation and vulnerability analysis. Each node and link in the network were equipped with attributes, such as coordinates, and administrative regions derived from the traffic data. Node data included node IDs assigned within the transportation network and their respective X and Y coordinates (see

Table 1. Summary of node data.

Node	X-Coordinate	Y-Coordinate	Data3
1	309905	554098	11010
2	312213	551430	11020
3	310307	548722	11030
4	315001	550794	11040
5	318852	549698	11050
6	316844	553737	11060

). Additionally, a Data3 custom attribute was added to represent a 5-digit administrative region code (city, district, or municipality). To ensure spatial accuracy, the coordinate data were transformed into the EPSG:4326 (WGS84) coordinate reference system. The converted coordinates, expressed in latitude and longitude, served as the basis for constructing the network graph. Thus, each node was precisely positioned within the graph, reflecting real-world geographic and administrative properties.

The link data are composed of the starting and ending node IDs, representing each link’s origin and destination (see

Table 2. Summary of link data.

From	To	Length
1	221688	0.01
1	227659	0.01
1	340675	0.01
2	221698	0.01
2	340765	0.01
2	340795	0.01
100003	100133	9.35
100004	100121	11.25
141178	142332	0.29
252543	252549	4.61

). The attribute Length specifies the distance associated with each link. For centroid connectors, the extension is standardized to 0.01 km, irrespective of their physical length. For all other links, the length is derived based on the actual physical distance between nodes, ensuring accurate representation of real-world conditions. This distinction allows for precise modeling of both functional and spatial aspects of the transportation network.

The weights required for network construction were derived from the total traffic volume (TotVol) collected from the traffic data as OD traffic volume.

Table 3. Summary of traffic volume data.

From	To	Length	Modes	Type	Lanes	VDF	TotVol
100016	488898	0.31	cp	103	1	22	2830
100016	488954	0.95	cp	103	1	22	2545
100045	318930	0.01	cp	103	2	12	15731
100045	678722	1.17	cp	103	2	12	15147
100046	100050	0.66	cp	103	2	12	14341
100046	318930	0.02	cp	103	2	12	13019
100047	100045	0.02	cp	106	1	10	2144

starts with the Node ID, indicating the origin and destination, and shows the TotVol as the total traffic volume. The data include details such as the IDs of the origin and destination nodes, transportation modes (e.g., car, pedestrian), and road classifications. Modes represent the types of transportation used in the network, including road-based modes such as cars and pedestrians (cp), as well as rail-based modes (r). Additionally, Type refers to the road grade code, where 103 indicates national highways and 101 represents expressways. This comprehensive dataset was used to construct the transportation network. The OD matrix was processed using EMME4 by aligning centroid connectors with traffic analysis zones (TAZs) and assigning vehicle classes accordingly.

3.2. Classification of Independent and Group Nodes

The constructed network graph was built as a directed graph based on from—to Node IDs. Independent nodes refer to all nodes comprising Korea’s transportation network. Single nodes were defined as all nodes within the constructed transportation network, totaling 48,067 nodes. Vulnerability analysis using single nodes allows for an assessment of impacts not confined to specific points but across the entire network. Group nodes were classified from the single nodes based on Korea’s administrative regions, resulting in 15 groups. These regions were geographically and administratively distinguished and categorized using the DATA3 attribute from the node data. Group nodes are utilized for aggregative analysis of connectivity and relationships among independent nodes within each region. They play a crucial role in identifying regional transportation vulnerabilities within the network.

3.3. Definition of Vulnerability Functions

The vulnerability function quantitatively represents the relationship between a specific node and its neighboring nodes. Vulnerability is calculated based on the neighboring nodes connected to each node. Bozzo et al. defined vulnerability using the size of a selected node set $T$ and the size of the neighboring node set $N\left(T\right)$, as expressed by the following equation [34]:

$$v_G\left(T\right)= \mid T\mid -\mid N\left(T\right)\mid$$

(1)

where $\mid T\mid =\mathrm{T}\mathrm{h}\mathrm{e} \mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r} \mathrm{o}\mathrm{f} \mathrm{n}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n}\mathrm{c}\mathrm{l}\mathrm{u}\mathrm{d}\mathrm{e}\mathrm{d} \mathrm{i}\mathrm{n} \mathrm{s}\mathrm{u}\mathrm{b}\mathrm{s}\mathrm{e}\mathrm{t} T$;

$N\left(T\right)=\mathrm{T}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{e}\mathrm{t} \mathrm{o}\mathrm{f} \mathrm{n}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{b}\mathrm{o}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{n}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{n}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{t}\mathrm{o} \mathrm{e}\mathrm{a}\mathrm{c}\mathrm{h} \mathrm{n}\mathrm{o}\mathrm{d}\mathrm{e} \mathrm{i}\mathrm{n} T$;

$\mid N\left(T\right)\mid =\mathrm{T}\mathrm{h}\mathrm{e} \mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r} \mathrm{o}\mathrm{f} \mathrm{n}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{b}\mathrm{o}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{n}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n} N\left(T\right)$.

Here, $\mid T\mid$ represents the size of the node set $T$, which indicates the number of specific independent nodes, while $\mid N\left(T\right)\mid$ denotes the size of the neighboring node set. We applied this function to transportation networks to calculate the vulnerability of individual transportation nodes as well as grouped regional transportation nodes. If the result is positive, it indicates that the selected node is relatively isolated compared to its neighboring nodes. Conversely, a negative result indicates that the selected node is closely connected to its neighboring nodes.

The proposed approach evaluates the vulnerability of transportation networks not only by assessing the importance of individual nodes but also by grouping nodes into regional clusters to evaluate their collective vulnerabilities. In this study, vulnerability is defined based on the extent of connections a specific region has with its neighboring nodes.

3.3.1. Vulnerability of Individual Nodes

The vulnerability of single nodes is calculated as follows, allowing for the derivation of individual vulnerability values within the network. Specifically, it represents how vulnerable each transportation node is on an individual basis within the network.

$$v_i= \mid i\mid -\mid N\left(i\right)\mid =1-\mid N\left(i\right)\mid$$

(2)

where $i=\mathrm{n}\mathrm{o}\mathrm{d}\mathrm{e} i \mathrm{s}\mathrm{i}\mathrm{z}\mathrm{e}$;

$N\left(i\right)=$ A set of neighboring nodes associated with the node i;

$\mid N\left(i\right)\mid =\mathrm{N}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r} \mathrm{o}\mathrm{f} \mathrm{n}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{b}\mathrm{o}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{n}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{s},\mathrm{i}.\mathrm{e}. \mathrm{d}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{n}\mathrm{o}\mathrm{d}\mathrm{e} i$.

Here, $v_i$ represents the vulnerability of node $i$, and $\mid N\left(i\right)\mid$ indicates the number of neighboring nodes connected to node $i$. This formula evaluates how individually vulnerable a specific node is within the network. The fewer the neighboring nodes, the higher the vulnerability value, which signifies that the node is more vulnerable within the network. In contrast, nodes with more connections in the network are considered less vulnerable.

• If $v_i$ = 0, the node is connected to a single neighboring node. This indicates a certain level of connectivity but still signifies a vulnerable state within the network.
• If $v_i$ < 0, the node is identified as a vulnerable point in the network the node is considered structurally vulnerable. The more negative the value, the fewer external connections the node has relative to its local structure, indicating increased isolation and potential disruption risks.

In other words, nodes with highly negative vulnerability scores are more likely to hinder inter-regional flows and reduce the overall robustness of the transportation network. Analyzing the vulnerability of a single node can be applied to identify key factors causing bottlenecks in transportation networks or to assess underserved areas.

3.3.2. Vulnerability of Group Nodes

The function for analyzing the network vulnerability of group nodes on a regional scale is as follows. This allows for the calculation of vulnerability values for each region within the network. Specifically, it evaluates how vulnerable a particular region is in terms of its connections to external regions. In other words, it indicates the degree to which the nodes within a region are connected to nodes in other regions, determining the region’s vulnerability.

$$v\left(T\right)= \mid T\mid -\mid N\left(T\right)\mid$$

(3)

where $\mid T\mid =\mathrm{N}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r} \mathrm{o}\mathrm{f} \mathrm{n}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{s} \mathrm{i}\mathrm{n} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{s}\mathrm{e}\mathrm{t} T$;

$N\left(T\right)=$ A set of neighboring nodes connected to the nodes in set $T$;

$\mid N\left(T\right)\mid =\mathrm{S}\mathrm{i}\mathrm{z}\mathrm{e} \mathrm{o}\mathrm{f} \mathrm{n}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{b}\mathrm{o}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{n}\mathrm{o}\mathrm{d}\mathrm{e}\mathrm{s} \mathrm{w}\mathrm{h}\mathrm{o}\mathrm{s}\mathrm{e} \mathrm{s}\mathrm{e}\mathrm{t} \mathrm{i}\mathrm{s} \mathrm{c}\mathrm{o}\mathrm{n}\mathrm{n}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{t}\mathrm{o} \mathrm{t}\mathrm{h}\mathrm{e} \mathrm{o}\mathrm{u}\mathrm{t}\mathrm{s}\mathrm{i}\mathrm{d}\mathrm{e}.$

Here, $v\left(T\right)$ represents the vulnerability of the group node set $T$, and $\mid N\left(T\right)\mid$ indicates the number of neighboring nodes connected externally to the set. This formula evaluates how connected or disconnected a group of nodes is compared to other groups in the network. If the nodes in set $T$ are well connected externally, the vulnerability value will be high. Conversely, if external connections are limited, the vulnerability value will be low.

• If $v\left(T\right)$ > 0, the region is relatively isolated and in a vulnerable state within the network. This means the nodes within the set lack sufficient external connections, making the region vulnerable. In transportation networks, poorly connected regions may lead to disruptions in traffic flow, social mobility, and economic activities between regions.
• If $v\left(T\right)$ < 0, the region is well connected to its surroundings, indicating lower vulnerability within the network. Nodes within the set act as strong connection hubs, reducing their susceptibility to external disruptions. Such regions play a key role in supporting inter-regional connectivity within the network.

As a result, we analyzed the structural characteristics and regional vulnerabilities of Korea’s transportation network using the vulnerability evaluation results for both single and group nodes. Nodes with positive vulnerability values in the single-node vulnerability function were classified as highly vulnerable nodes within the network, often corresponding to bottleneck points in traffic flow. Regions with negative vulnerability values in the group-node vulnerability function were identified as major connection hubs, supporting the overall network stability.

3.4. Comprehensive Assessment of Transportation Network Vulnerability

We conducted a vulnerability analysis of Korea’s transportation network to identify critical points and regions that require attention, proposing a methodology to support transportation policy analysis. This comparison allowed us to identify nodes with higher vulnerability, which may act as bottlenecks in traffic flow, and to evaluate the vulnerability of group nodes to assess regional connectivity and network stability. By comparing the vulnerabilities of individual nodes and regional clusters, we comprehensively analyzed the key vulnerability points within the transportation network. This step ensures a holistic understanding of the network’s structural weaknesses.

By comparing the vulnerabilities of single nodes and group nodes, we performed a comprehensive analysis to identify key vulnerable points in the transportation network. The analysis of single-node vulnerabilities identified specific weak nodes, while the group-node vulnerability analysis assessed the stability and connectivity of regions based on their inter-regional links. The vulnerability function played a critical role in quantifying the relationships between nodes and their neighbors, enabling the evaluation of both individual node and regional vulnerabilities.

The overall analysis of vulnerable nodes and regions provides a framework for policy analysis aimed at improving the efficiency and flow of Korea’s transportation network. This evaluation highlights the vulnerabilities of critical transportation hubs, such as roads and railways, offering foundational data for infrastructure improvements and policy responses.

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.

• 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 buk-do, outside the Seoul metropolitan area (see

Table 4. Single-node vulnerability results summary (in order of low vulnerability).

Node	Region	Original Value	Z-Score Value	X- Coordinate	Y- Coordinate
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	Gyeongsangbuk-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

).

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.

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. Group-node vulnerability results (sorted by highest vulnerability).

Region	Original Value	Z-Score Value
Gyeonggi-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

). 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.

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 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.

5. Discussion

We utilized the vulnerability function to quantitatively analyze Korea’s transportation network, objectively assessing the structural characteristics of the network and regional disparities in vulnerability. The results show that central regions, such as Seoul, maintain network stability and serve as critical hubs, whereas most regional areas exhibit relatively lower vulnerability. This indicates stronger connectivity in these areas, emphasizing the need for policy efforts to address regional imbalances.

In particular, we confirmed that the vulnerability function is an effective and objective tool for quantitatively evaluating the likelihood of disconnection for specific nodes or regions, unlike traditional centrality measures. Gyeonggi exhibited the highest level of structural vulnerability, indicating a strong reliance on concentrated connections within the transportation network. Although non-capital regions display lower structural vulnerability, their comparatively limited accessibility to transport services remains a critical concern for policy development.

Through a review of the literature, we observed that previous approaches have often focused on centrality analysis and simulations. In contrast, we modeled vulnerability using graph theory and mathematical functions, allowing us to intuitively identify weaknesses in the network through the derived results. This analysis revealed the regional imbalances within the transportation network and demonstrated its potential to contribute significantly to improving the efficiency of regional transportation systems, both academically and in policymaking.

The proposed methodology offers generalizability as a methodological advantage.

Its structural foundation, independent of flow-specific assumptions, allows for application across varying spatial and modal transportation systems, providing a basis for comparative analysis. Future research should expand upon the proposed vulnerability function and analytical method by applying them to other countries or large-scale urban networks to compare vulnerabilities across different transportation environments. Additionally, policy simulations based on the proposed vulnerability index would provide valuable insights for verifying the effectiveness of specific transportation improvement measures and policy interventions.

In conclusion, we propose a robust tool for objectively and quantitatively evaluating the structural characteristics of transportation networks using the vulnerability function. This tool extends beyond academic analysis and provides a crucial foundation for practical transportation policy and regional development aimed at achieving balanced growth.

6. Conclusions

We quantitatively analyzed Korea’s transportation network using a vulnerability function, enabling an intuitive assessment of regional vulnerabilities within the network. The analysis revealed that the metropolitan areas, including Gyeonggi-do and Seoul, function as the central axis of the network, exhibiting high vulnerability and playing a critical role in maintaining network stability. These regions demonstrate concentrated connectivity, indicating a structure that may be more susceptible to disruptions in the event of node failures.

In contrast, regional metropolitan cities such as Daejeon, Gwangju, and Gyeongsangnam-do exhibit low vulnerability, indicating relatively stronger connectivity within the network. Notably, Daejeon recorded the lowest vulnerability score, highlighting the need for policy efforts to maintain inter-regional connections and support redundancy.

The analysis of individual nodes further revealed that major nodes in the metropolitan areas exhibit higher vulnerability, functioning as structurally critical yet potentially fragile hubs within the network. In comparison, nodes in the peripheral areas of region recorded relatively lower vulnerability, suggesting stronger inter-node connectivity and a reduced risk of network disconnection that could hinder regional mobility and accessibility.

This study demonstrated the effectiveness of the vulnerability function as a tool for efficiently identifying vulnerable regions within the network. The results provide an objective framework for evaluating regional imbalances and highlight the practical utility of this analysis in transportation network design and policymaking. In conclusion, this study quantitatively evaluated network vulnerabilities and offers foundational insights to enhance regional connectivity and transportation efficiency. It serves as a robust tool for promoting balanced development within the transportation network and provides actionable directions for improving vulnerable regions.

Future research could extend the application of the vulnerability function to other countries or diverse transportation environments to compare network vulnerabilities across various contexts. Additionally, policy simulations based on the proposed vulnerability index could provide concrete recommendations for improving transportation networks and assessing the effectiveness of policy interventions.