Runway Incursion Risk Propagation Model Based on Complex Network Theory

Abstract

Runway incursions remain a major threat to airport surface safety, and effective prevention depends on the accurate identification of causal risk factors and their interaction mechanisms. However, existing studies have mainly focused on isolated risk factors or static causal relationships, offering limited insight into the hierarchical structure and dynamic propagation of runway incursion risk in complex operational environments. To address this gap, this study proposes a quantitative framework for runway incursion risk analysis by integrating grounded theory and complex network theory. Published runway incursion cases in the Chinese civil aviation system from 2022 to 2025 were systematically analyzed through open coding, axial coding, and selective coding, resulting in a hierarchical indicator system comprising five main categories, twelve subcategories, and 112 risk indicators. Based on this system, a runway incursion causal network was constructed to characterize the causal interdependencies among risk factors. Node importance was evaluated using a TOPSIS-based multi-criteria method integrating multiple network metrics, and a load-distribution-based propagation mechanism was introduced to quantify the risk propagation probability and risk propagation intensity of each node. The results indicate that insufficient night lighting (N99), taxi-route memory errors (N14), ambiguous controller instructions (N1), and excessive controller workload (N10) exhibit relatively high risk propagation probability and risk propagation intensity, indicating their critical roles in the evolution and cascading propagation of runway incursion risk. These findings demonstrate that the proposed framework can effectively capture both the structural importance and propagation characteristics of causal risk factors. Therefore, this study provides quantitative support for understanding runway incursion risk evolution and for developing targeted prevention strategies and post-incident response measures to improve runway safety management.

1. Introduction

In recent years, China’s civil aviation industry has experienced rapid growth, accompanied by an increasing demand for transport airports and runway construction. According to the latest statistics released by the Civil Aviation Administration of China, by the end of 2024, the number of transport airports in China had reached 263, with a total of 290 runways. In the same year, the number of aircraft take-offs and landings approached 12.4005 million, exceeding the pre-pandemic peak of 11.6605 million recorded in 2019 [1]. These data indicate that China’s air transport industry has entered a stage of steady recovery and continued expansion. However, with the enlargement of airport infrastructure and the continuous growth of flight operations, runway incursion risk has also become increasingly prominent. Previous studies have shown a positive correlation between airport traffic volume and runway safety risk. According to the report of the National Civil Aviation Safety Committee, Sub-Committee on Runway Incursions, a 20% increase in airport traffic volume (from four to five aircraft) corresponds to an approximately 140% increase in runway incursion potential, indicating that runway incursion risk increases disproportionately relative to traffic volume [2].

Because unsafe events are usually driven by multiple interacting risk factors, many scholars have conducted extensive research on runway incursions. David Kaminski-Morrow analyzed runway incursion cases caused by communication interruptions and showed that communication problems were an important cause of runway incursions [3]. Song reviewed the application of various methods and measures for preventing runway incursions and concluded that insufficient and untimely preventive measures were important contributing factors [4]. Wu developed a dynamic Bayesian network risk prediction model integrated with reinforcement learning and pointed out that the lack of proactive risk prediction could lead to frequent runway incursion events [5]. Zhao proposed an improved lightweight YOLOv3 airport object detection model based on an attention mechanism to improve airport target detection accuracy and real-time performance [6]. Liang improved the HFACS-RI framework and applied it to the analysis of worldwide cases, thereby providing theoretical support for runway incursion prevention [7]. Yang investigated runway incursion detection technology based on NSCT and the semi-tensor product, providing methodological support for the prevention of runway incursion events [8]. To clarify the relationships among influencing factors, Yuan Leping analyzed multiple runway incursion cases from four perspectives and identified correlations among more than 140 risk factors by examining factor interactions in the cases [9]. Shen used ADS-B technology to predict the timing and conflicts of impending runway incursions [10]. Pan analyzed runway incursion risk factors based on gray relational analysis and found that human factors were the core contributors [11]. Tang identified personnel-related risk factors through systematic analysis and constructed a quantitative risk assessment indicator system [12].

In parallel, complex network theory has been widely applied in medicine, genetics, transportation, and other fields by abstracting complex systems into network structures to address practical problems. Wang Ping proposed a prediction model combining complex networks and recurrent neural networks, and experimental results showed that this model outperformed traditional methods in both accuracy and stability, demonstrating significant engineering value [13]. Sun’s team constructed a framework for calculating the complexity of autonomous driving road test scenarios by integrating operational design conditions with the analytic hierarchy process and verified the effectiveness and rationality of the model through actual road tests [14]. In civil aviation, research on aviation network topology has also attracted considerable attention. Wang’s quantitative analysis of air traffic situation risk confirmed that aircraft aggregation, proximity to key nodes, and flight-segment deviation were significantly positively correlated with risk values [15]. Bai Yu constructed a directed weighted route network model for the Chengdu–Chongqing airport cluster and showed that the route network exhibited small-world characteristics while still requiring further structural optimization [16]. Cao Boyang applied a complex network approach to analyze the risk factors of unsafe incidents in civil aviation maintenance units, and the results visualized the causal relationships among unsafe events, providing a reference for risk analysis and control in civil aviation maintenance [17]. Zhang used a complex network method to analyze network evolution from the perspectives of node centrality, association structure, hierarchical characteristics, and community structure, and further examined the influencing factors through geographic detector analysis [18]. Mei Aoran proposed an analytical method for identifying association rules among risk factors and the dynamic evolution process of risk propagation in runway landing events, thereby providing a useful reference for aircraft operation safety management [19]. Fang monitored real-time air traffic flow and investigated the characteristics of global air traffic networks by constructing a complex airspace traffic network for airport terminal areas and improved the accuracy of airport delay prediction through a spatiotemporal graph convolution model [20].

Overall, existing studies have provided valuable insights into the causes, detection methods, and assessment approaches related to runway incursions. However, research that systematically integrates the identification of causal risk factors with the analysis of their structural interdependencies and propagation characteristics remains limited. Therefore, it is necessary to develop a framework capable of revealing both the causal structure and dynamic evolution of runway incursion risk, so as to provide more effective support for runway safety prevention and control.

2. Construction of the Runway Incursion Risk Indicator System

The grounded theory analysis in this study is based on a systematically collected dataset of runway incursion incident reports. The primary data sources are investigation reports, safety bulletins, and operational records from the Chinese civil aviation system spanning the years 2022–2025. A detailed description of the dataset, including its composition and scope, is provided in Section 4.1. Case selection followed these criteria to ensure relevance and analytical depth:

• The event was explicitly classified as a runway incursion according to ICAO definitions;
• The case narrative contained sufficient detail to allow for the extraction of causal risk factors and their relationships;

As a systematic qualitative research approach, grounded theory enables researchers to derive an objective and comprehensive theoretical framework from empirical cases through a rigorous three-stage coding procedure (data collection, analytical coding, and theory construction) [21]. In this study, we systematically collect and analyze representative runway incursion cases from airports worldwide and process the raw case materials using a three-level coding scheme. As illustrated in Figure 1, the resulting runway incursion risk indicator system is structured hierarchically. First, open coding is performed to extract initial concepts, yielding 112 risk indicators (see

Table A1. Runway incursion risk indicators.

Number	Category	Definitions and Interpretations	Conceptual Connotation
1	Controller factor	In the process of aircraft or vehicle operation control, there are various factors that increase the risk of runway incursion due to deficiencies or deviations in the cognition, decision-making, work, communication and professional status of air traffic controllers	N1: Ambiguous controller instructions N2: Instructions delivered too rapidly N3: Use of non-standard phraseology/terminology N4: Unfamiliarity with special operations N5: Fatigue-induced inattention N6: Failure to monitor radar/surface surveillance displays N7: Lack of situational awareness N8: Failure to correct unit errors in a timely manner N9: Insufficient multitasking capability N10: Excessive controller workload N11: Failure to strictly implement readback/hearback procedures N12: Inexperience of newly assigned personnel
2	The pilot factor	In the course of aircraft operation, due to the pilot’s understanding of control instructions, judgment of his own position and decision-making errors in taxiing, take-off, landing and other links, the scope of various factors that cause the aircraft to mistakenly enter the runway, stay improperly on the runway or collide with other aircraft or vehicles	N13: Misunderstanding of ATC instructions N14: Taxi-route memory errors N15: Failure to read back key instructions N16: Reliance on habit without cross-checking N17: Non-compliance with standard taxi procedures N18: Incorrect identification of runway markings N19: Failure to use airport charts/airport moving-map aids N20: Cockpit Resource Management (CRM) breakdown N21: Insufficient foreign-language communication proficiency N22: Failure to monitor the movement of ground vehicles N23: Excessive taxi speed at night N24: Incorrect execution of pre-take-off checks N25: Failure to notice NOTAM updates/changes N26: Failure to use taxi guidance lights N27: Unclear division of labor within the unit/crew
3	Ground vehicle personnel factors	The driver of the airport ground support vehicle and the accompanying operators have deviations in the perception and behavior of safety boundaries in airport ground operations (such as taxiway driving, parking space operations, runway perimeter support, etc.), causing the vehicle to mistakenly enter the runway, runway protection area, or conflict with aircraft and other ground facilities	N28: Runway entry without clearance N29: Failure to monitor ATC frequencies N30: Non-compliance with vehicle speed limits N31: Failure to taxi via the assigned route N32: Failure to follow the designated route N33: Rushing to depart under time pressure N34: Failure to observe aircraft movements N35: Construction vehicles lack warning markings/devices
4	Communication system factors	The scope of technical defects, rule loopholes, signal interference or improper use of various communication means used for information transmission in airport operation leads to the failure of information transmission methods between controllers, pilots, and ground vehicle personnel, resulting in runway incursion	N36: Headset/microphone malfunction N37: Radio signal interference N38: Speech-recognition system misinterprets instructions N39: Backup communication equipment not enabled N40: Frequency congestion causes communication delays N41: Non-unified cross-department communication channels N42: CPDLC not deployed (controller–pilot data link communication)
5	Monitor device factors	All kinds of equipment used to monitor the position of aircraft, ground vehicles, personnel and runway status in real time are subject to the category of risk factors that cause controllers to be unable to accurately grasp the status of the runway due to technical performance defects, data processing deviations, improper operation and maintenance, etc., and then cause runway incursion.	N43: ADS-B signal loss N44: Blind spots in airport surface surveillance radar (ASDE) coverage N45: Unreasonable alarm threshold settings N46: MLAT system not installed (multilateration unavailable) N47: Insufficient monitoring system refresh rate N48: Runway incursion alert not triggered N49: Lack of AI-based risk prediction capability N50: Tower display information latency
6	Airport guidance system factors	Various guidance facilities and systems used to guide aircraft and ground vehicles to move and position safely on the ground at airports cause navigators to misjudge the position, path or runway status due to design defects, maintenance omissions, insufficient information deviations and other problems, which in turn leads to a series of risk factors that lead to mistakenly entering the runway or deviating from the specified path.	N51: Faded taxiway signage/markings N52: Runway centerline lighting malfunction N53: Stop-bar lights malfunction N54: Hotspot warning signs not provided N55: Temporary closure areas not properly marked N56: Electronic charts not updated N57: A-SMGCS not deployed (Advanced Surface Movement Guidance and Control System) N58: Runway Status Lights (RWSL) not activated N59: Substandard lighting in construction areas N60: Complex design of taxiway–runway intersections
7	Training and qualification factors	It covers all elements of the training system, qualification management and competency maintenance of pilots, controllers, ground staff and airport vehicle drivers	N61: Insufficient controller simulation training N62: Pilots lack dedicated runway incursion prevention training N63: Lack of multi-department joint exercises/drills N64: Excessive interval between recurrent trainings N65: Training content does not cover typical cases N66: Lack of situational awareness assessment N67: Insufficient onboarding training for new staff N68: Lack of foreign-language radiotelephony training N69: VR-based simulation training not introduced N70: Formalistic evaluation of training effectiveness
8	Run program factors	A series of standardized operating rules, coordination mechanisms and emergency response procedures formulated to standardize the use process of key areas such as airport runways and taxiways and ensure the orderly and controllable activities of aircraft, vehicles and personnel	N71: Unreasonable taxi-route design/setting N72: Unclear cross-department responsibilities N73: Night-operation risks not specifically controlled N74: Disorganized temporary procedures during construction N75: Lack of an emergency plan for runway incursions N76: Imperfect low-visibility operating procedures (LVO) N77: Failure to enforce standard phraseology N78: Insufficient resource allocation during peak traffic periods N79: Runway Safety Team (RST/RSS) mechanism not implemented N80 N81: Delayed safety information sharing N82: No risk early-warning indicator database established
9	Safety culture factors	It runs through the scope of safety values and codes of conduct for airport flight crews, air traffic control personnel, ground handling support, management departments and other personnel.	N83: Low willingness among staff to report hazards N84: Management insufficiently prioritizes risk N85: Safety meetings become formalities N86: No anonymous reporting system established N87: Non-transparent reward-and-punishment mechanism N88: Failure to promote a just culture
10	Meteorological factors	Weather conditions such as visibility, snowfall, wind, etc., may interfere with the judgment, operation or equipment operation of relevant personnel on the runway, thereby increasing the risk range of runway incursion probability.	N89: Fog with visibility below minimum standards N90: Heavy rainfall affects taxi control N91: Crosswinds increase deviation/overrun risk N92: Thunderstorms disrupt communications N93: Low cloud obscures runway lights/visual cues N94: Snow-covered taxiway signs N95: Adverse airfield physical environment
11	Airport environmental factors	Due to problems such as unreasonable design, unclear signage, and spatial conflict of the airport’s physical layout, facility identification, and airspace structure, it interferes with the judgment of relevant personnel on the location and route, thereby increasing the risk range of runway incursion probability.	N96: Excessive runway/taxiway intersections N97: Construction areas encroach on taxi routes N98: Airport expansion leads to layout changes N99: Insufficient night lighting N100: Perimeter obstacles restrict line of sight
12	Information transmission factors	Between the controllers, pilots, ground staff, airport dispatchers, etc., involved in the operation of the runway, due to untimely, inaccurate, incomplete or misunderstanding of information transmission, the relevant personnel misjudged the status of the runway and other key information.	N101: Flight schedule inconsistent with electronic systems N102: Delayed NOTAM updates N103: Real-time flight dynamics not shared N104: Conflicts between voice instructions and digital clearances N105: Digital taxi guidance not used N106: Lack of coordination between tower and apron control N107: Critical instruction timestamps not recorded
			N108: Unclear handover of ATC and ground-handling responsibilities N109: Missing emergency response coordination mechanism N110: No regular runway safety meetings held N111: Construction contractors fail to notify operational plans N112: Airline information not synchronized with airport systems

). Next, axial coding is applied to identify relationships among concepts and to aggregate them into higher-order categories. Finally, selective coding is conducted to refine and validate the core structure, resulting in five core categories—personnel factors, airport equipment factors, information and coordination factors, environmental and meteorological factors, and organizational and management factors-along with twelve sub-categories (see

Table 1. Main categories of spindle coding of runway incursion risk factors.

Number	Main Category	Affect the Category of Relationships
1	Personnel factors	Standard land-air calls are not used; controller workload; the unit did not follow the taxiing route;
2	Organizational and management factors	Inadequate ground support; new employee management is not timely
3	Airport equipment factors	Technical condition of equipment; system failure
4	Environmental and meteorological factors	Weather reasons
5	Information and coordination factors	Errors occur in the communication and information transmission process of decision-making

).

To construct the causal network, the causal links between risk factors must be objectively extracted from the textual case reports. This process followed a structured protocol to ensure reproducibility and reliability.

Operational Definition of Causality: A causal statement was operationally defined as a description in the event narrative where

• Risk Factor A is explicitly stated or strongly implied to temporally precede and directly contribute to the occurrence or exacerbation of Risk Factor B;
• The narrative logic indicates that B would not have occurred, or would have been less severe, in the absence of A. Mere co-occurrence or contextual association without a directed, generative link was not coded as a causal relationship.

Coding Procedure: Two researchers independently reviewed the same set of case reports. They first identified all risk factors present in a case (based on the established 112-indicator system) and then analyzed the narrative to identify all pairwise cause-effect links between these factors.

Inter-Coder Reliability and Consensus: After the initial independent coding, the two coders compared their identified causal links for each case. Discrepancies were discussed with reference to the operational definition. A third senior researcher was consulted to resolve any persistent disagreements. This consensus-building process yielded the final set of validated causal links for each case. The inter-coder reliability, measured by Cohen’s Kappa on a subset of 20 cases prior to consensus, was k = 0.78, indicating substantial agreement.

Edge Weight Calculation: For the entire dataset, the frequency of each unique directed causal link (e.g., Factor i → Factor j) across all cases was summed. This frequency count was directly used as the weighted adjacency matrix element $a_{ij}$ (as defined in Equation (2)), representing the empirical strength of that causal pathway observed in the historical data.

To ensure the methodological rigor of the grounded theory analysis, we explicitly assessed theoretical saturation and implemented a coding validation procedure.

• Assessment of Theoretical Saturation: After the initial coding framework (112 first-order concepts and the higher-order categories) was established from the first batch of cases, we analyzed additional, sequentially selected case reports. The purpose was to determine if new first-order concepts, categories, or substantial modifications to the existing category relationships emerged. This iterative process continued until no new substantive insights were generated from the additional data, at which point the coding framework was considered theoretically saturated.
• Coding Validation and Reliability: To enhance the credibility of the coding results, two researchers independently performed open and axial coding on a randomly selected subset of cases (approximately 30% of the total dataset). They then compared their derived concepts and categories. Discrepancies were discussed and resolved through consensus, referring back to the original text. The inter-coder agreement, measured by Cohen’s Kappa coefficient, reached 0.81, indicating an almost perfect level of agreement. This process helped to minimize individual coder bias and strengthen the validity of the final risk indicator system.

3. Model Development

3.1. Determining Edge Connectivity and Directionality

There is a causal relationship between different risk factors, and a series of causal chains are obtained according to the causal relationship [22]. In the network model, the risk factor represents the network nodes, and the causal chain is the edge of the network. The existence of an edge is based on causation, and the weight of an edge is the number of times the causal relationship occurs in a case. The causal relationship between the various risk factors in these events was analyzed, and the number of occurrences was counted. For example, if “Unit Cognitive Error” occurs in multiple events due to “Non-standard Control Instructions”, then the weight of this edge increases accordingly, defined as matrix N.

$$N=\left[\begin{array}{cccc}{n}_{11}& n_{12}& \dots & n_{1m}\\ n_{21}& n_{22}& \dots & n_{2m}\\ ⋮& ⋮& \ddots & ⋮\\ n_{m1}& n_{m2}& \dots & n_{mm}\end{array}\right]$$

(1)

If $n_{ij}$ = 1 in the matrix, node i and node j are connected and i points to j, and if $n_{ij}$ = 0, indicates that node i and node j are not connected.

3.2. Determination of Directed Edge Weights

The directed edge weight can be defined in a reproducible way as the frequency with which a causal relationship occurs across the sampled cases. Suppose there are K runway incursion cases, and nodes i and j represent two risk factors.

Let $c_{ij}^{(k)}$ denote the number of times that risk factor i is identified as a cause of risk factor j in case k (typically 0 or 1, but multiple occurrences can also be allowed). The directed edge weight is defined as:

$$a_{ij}={\displaystyle \sum _{k=1}^K{c}_{ij}^k},(i,j=1,2,\dots ,m)$$

(2)

Accordingly, the weighted adjacency matrix is $A=\left[a_{ij}\right]$.

3.3. Causal Network Model Construction

Multiple risk factors jointly contribute to the occurrence of runway incursion events, and causal relationships exist among different risk factors. By incorporating all risk factors and their causal links into a unified network model, the runway incursion causal complex network can be visualized using Gephi 0.9.0, as shown in Figure 2.

3.4. Complex Network Model Characteristic Analysis

The network model consists of 112 nodes and 270 directed weighted edges, where nodes represent runway incursion risk factors, and an edge between two nodes indicates a causal relationship between the corresponding factors.

To characterize the structural properties of the runway incursion risk network, node degree, network density, clustering coefficient, and betweenness centrality were calculated. Degree describes the direct connectivity of a node and, in directed networks, can be further divided into in-degree and out-degree. Density reflects the overall compactness of the network by comparing the observed number of links with the total number of possible links. The clustering coefficient measures the extent to which neighboring nodes tend to form closed triangular structures, indicating local cohesiveness. Betweenness centrality quantifies the extent to which a node lies on the shortest paths between other nodes, thereby reflecting its mediating effect in risk propagation. These metrics are widely used to reveal node importance and structural characteristics in complex networks.

The calculation procedures of the following complex network model characteristic were based on Ref. [23].

1.

Node Degree

Nodes with high out-degree act as primary risk “emitters”, whereas nodes with high in-degree are more likely to be triggered by multiple upstream factors and thus represent typical downstream outcomes. The calculation formula is as follows:

$$k_i^{out}={\displaystyle \sum _{j=1}^n{a}_{ij}},k_i^{in}={\displaystyle \sum _{j=1}^n{a}_{ij}},k_i=k_i^{out}+k_i^{in}$$

(3)

2.

Network density

A low density implies that direct interactions among risk factors are limited, so effective mitigation should prioritize the few dominant links and nodes that concentrate most causal dependencies.

The specific formula is given by:

$$p={\displaystyle \frac{m}{n(n-1)}}$$

(4)

3.

Clustering Coefficient

High-clustering nodes tend to sit inside tightly connected local structures, where a single abnormal factor can rapidly activate neighboring risks and produce localized cascading effects.

$$C_i={\displaystyle \frac{2E_i}{k_i(k_i-1)}}$$

(5)

4.

Network Diameter and Average Path Length

Smaller average path length indicates higher transmission efficiency of risk signals in the network, highlighting the need for early intervention at upstream nodes to prevent fast multi-step propagation.

The network diameter is defined as the maximum shortest-path distance between any two causal nodes in the network, and it can be expressed as:

$$D={\max }_{ij\in n}(d_{ij})$$

(6)

$$L={\displaystyle \frac{{\displaystyle \sum _{i\ne j}{d}_{ij}}}{n(n-1)}}$$

(7)

where L denotes the average path length of the network, and d_ij represents the distance (shortest-path length) between any two nodes i and j in the network.

5.

Betweenness Centrality

Nodes with high betweenness centrality function as structural “bridges” connecting different causal pathways and controlling them can significantly reduce the network-wide spreading potential of runway incursion risk:

$$F_{\mathrm{ab}}(i)={\displaystyle \frac{N_{\mathrm{ab}(i)}}{N_{\mathrm{ab}}}}$$

(8)

where F_ab(i) denotes the betweenness centrality of node i; N_ab(i) is the number of shortest paths between nodes a and b that pass through node i; and Nab is the total number of shortest paths between nodes a and b. Based on these definitions, the betweenness centrality of each node in the runway incursion causal network model is calculated.

3.5. Node Importance Evaluation

Suppose a complex network has a total of a node, and each node is described by b characteristic indicators, and the set of nodes is expressed as G = {G₁, G₂, G₃ … G_a}, H_in represent the value of the n-th feature indicator of node i, where i = 1, 2, 3 … a, n= 1, 2, 3 … b. The characteristic indicator matrix in the runway incursion risk factor network is:

$$H=\left[\begin{array}{cccc}{H}_{11}& H_{12}& \dots & H_{1\mathrm{b}}\\ H_{21}& H_{22}& \dots & H_{2\mathrm{b}}\\ ⋮& ⋮& \ddots & ⋮\\ H_{\mathrm{a}1}& H_{\mathrm{a}2}& \dots & H_{\mathrm{ab}}\end{array}\right]$$

(9)

Normalizing matrix H can be obtained as follows:

$$Z_{\ln }={\displaystyle \frac{H_{\ln }-H^{{\min }_{\ln }}}{H^{{\max }_{\ln }}-H^{{\min }_{\ln }}}}$$

(10)

The matrix after Z normalization is as follows:

$$Z=\left(\begin{array}{ccc}{z}_{11}& \dots & z_{1m}\\ ⋮& \ddots & ⋮\\ z_{n1}& \dots & z_{nm}\end{array}\right)$$

(11)

The TOPSIS method is used to calculate the importance of nodes in the network, and the specific formula is as follows:

$$U_l={\displaystyle \frac{b_l^{-}}{b_l^{-}+b_l^{+}}}$$

(12)

$$D_t^{-}=\sqrt{{\displaystyle \sum _{j=1}^m{(q_{ij}-q_j^{\min })}^2}}$$

(13)

$$D_t^{+}=\sqrt{{\displaystyle \sum _{j=1}^m{(q_{ij}-q_j^{\max })}^2}}$$

(14)

A larger u-value indicates a greater impact on the network and vice versa.

3.6. Runway Incursion Risk Propagation Model Based on Load Allocation

Different nodes have different load risk capabilities, calculating the initial load and capacity of nodes in the network. The ability to determine the point load risk [23]. First, the initial load L_i of the node needs to be calculated, and the specific calculation formula is as follows:

$$L_i=F_{xy}(i)={\displaystyle \sum _{\mathrm{a}:x\mathrm{b}\ne t}\frac{N_{x,v}(t)}{N_{\mathrm{ab}}}}$$

(15)

where N_ab represents the total number of shortest paths from node a to node b; N_ab(i) represents the number of nodes that pass through in the shortest path from node a to node b.

If the load of the node i exceeds the capacity of the node i, it means that the node is at risk. On the contrary, there is no risk in the node i. Through the analysis, it can be seen that the capacity of the node is directly proportional to the initial load of the node in the function relationship, so the formula for calculating the node capacity is expressed as:

$${\mathcal{C}}_l=(1+\beta )L_l$$

(16)

Among them, β represents the tolerance coefficient, β > 0, combined with the universal data and, considering the convenience of calculation, the definition of β = 0.06 in this topic. In this load allocation model, the tolerance coefficient β is a crucial parameter that determines the additional capacity buffer of a node beyond its initial load. The value of β directly influences the robustness of the network: a larger β allows nodes to withstand more additional loads, making the network less susceptible to cascading failures triggered by a single node’s overload, albeit potentially overestimating the real system’s tolerance; a smaller β renders the network disproportionately fragile. The selection of β = 0.06 is not based on computational convenience but is informed by the common parameter range used in infrastructure network reliability studies. Furthermore, its appropriateness for maintaining stable identification results of key nodes is validated through the sensitivity analysis conducted in this study (see Section 4.3).

Assuming the node j is an adjacent node of the node i, then the amount of load assigned to the node j is expressed as:

$$\Delta L_{ji}=Li\times {\displaystyle \frac{c_{\mathrm{j}}-l_j}{2n{\in }_i(c_n-l_n)}}$$

(17)

where $c_j - L_j$ represents the load that the node can accommodate; $\sum _{n\in {\tau }_i}\left(c_n-L_n\right)$ represents the sum of all the loads that can be accommodated by nodes adjacent to the node i, and ${\displaystyle \frac{c_j-L_j}{\sum _{n\in {\tau }_i}\left(c_n-L_n\right)}}$ represents the proportion of the node i propagating the load across the node j.

When the load on node i exceeds the capacity of node i the node will be at risk, and the calculation formula is as follows:

$$P(L_{i^{\prime }})=\left\{\begin{array}{ll}0,\hfill & L_{i^{\prime }}\le C_i\hfill \\ {\displaystyle \frac{L_{i^{\prime }}-C_i}{(1+\partial )C_i-C_i}},\hfill & C_i<L_{i^{\prime }}\le (1+\partial )C_i\hfill \\ 1,\hfill & L_{i^{\prime }}>(1+\partial )C_i\hfill \end{array}\right.$$

(18)

where it is derived from the general principle of analysis and data, taking the parameter ∂ = 1.

The risk propagation ability of nodes is related to the characteristics of nodes themselves, and in this paper, three indicators of node degree, clustering coefficient and intermediate centrality are selected to calculate the risk propagation ability F of nodes, and the specific calculation formula is as follows:

$$F=\sqrt{{\displaystyle \frac{N_{\mathrm{deg}}^2+N_{clu}^2+N_{bet}^2}{3}}}$$

(19)

The formula for calculating the risk propagation probability of nodes is as follows:

$$Q =P\times F$$

(20)

• Q represents the comprehensive risk propagation value of a node, measuring its potential to spread risks across the entire network. The calculated result is a dimensionless value: higher values indicate stronger risk propagation capabilities when the node is activated (i.e., when a risk event occurs), meaning it is more likely to trigger cascading failure effects. By ranking nodes based on Q values, critical nodes with significant propagation influence can be identified and thus should receive prioritized attention in risk prevention and control efforts.
• P denotes the risk propagation probability of a node, representing the likelihood that its load exceeds capacity threshold when activated (risk event occurs), thereby triggering risk transmission to adjacent nodes. With values ranging from [0,1], P is calculated through the load-to-capacity ratio analysis.
• F indicates the risk propagation intensity, quantifying the impact scope or severity during risk propagation events. Its value spans [0,∞), determined by the combined evaluation of a node’s median centrality and edge weights.

4. Discussion

4.1. Dataset

The empirical analysis in this study is based on a curated dataset of 56 runway incursion incident reports. The data were collected from publicly released investigation reports, safety bulletins, and operational records within the Chinese civil aviation system, covering the period from January 2022 to December 2025. Case inclusion followed three primary criteria to ensure relevance and analytical depth:

• The event was officially classified as a runway incursion according to ICAO definitions;
• The investigative narrative contained sufficient detail to allow for the unambiguous extraction of risk factors and their causal relationships;
• The incidents occurred within the specified 2022–2025 timeframe to maintain data contemporaneity. This curated dataset formed the empirical foundation for the subsequent three-stage coding procedure.

The dataset encompasses several source types, including detailed investigation reports from aviation safety authorities, internal safety notices disseminated by airports and air traffic control units, and summarized operational records pertaining to runway operations. These texts were cleaned and standardized under a unified protocol. To ensure the reliability of the subsequent grounded theory analysis, the coding process incorporated rigorous validation procedures, including independent coding by two researchers and assessment of inter-coder agreement (Cohen’s Kappa = 0.81), as detailed in Section 2.

Following the “event, risk factor, causal chain” structure, causal linkages identified in the narratives were extracted and their frequencies across all cases were counted. These frequencies form the weighted adjacency matrix for network construction. Key network metrics (e.g., degree, betweenness, closeness centrality) were then computed. This processed dataset provides the foundation for the node importance evaluation and risk propagation modeling presented in the following sections.

4.2. Results

Based on the above dataset, a case study is conducted by reviewing the event narratives to identify causal linkages among risk factors and counting how frequently each cause–effect relationship occurs across all events. These frequencies are then used to determine the weights of directed edges in the network. For example, if “non-standard ATC instructions” are repeatedly found to lead to “crew cognitive errors” in multiple events, the weight of the corresponding causal edge is increased accordingly, thereby reflecting the strength and practical influence of this relationship in real operations. Partial edge weight values are presented in

Table 2. Partial Edge Weights.

LINK	N1	N2	N3	N4	N5	N6	N7	N8	N9	N10	…
N1	0	0	0	0	4	0	0	0	0	0	…
N2	0	0	0	0	0	0	0	2	0	0	…
N3	0	0	1	0	0	0	3	0	0	0	…
N4	0	0	0	0	0	0	0	1	0	0	…
…	…	…	…	…	…	…	…	…	…	…	…

. This table provides a transparent, quantitative snapshot of the core empirical finding: the transformation of narrative causal descriptions into countable, directed relationships. For example, the entry ‘4’ at the intersection of row N1 and column N5 indicates that across the entire case set, the risk factor “Ambiguous controller instructions” (N1) was explicitly identified as a direct cause of another factor “Fatigue-induced inattention” (N5) in four distinct incident reports.

The causal strength of the two factors in the runway incursion incident is expressed by the weight of the edge weight. Based on the statistics of causal relationship frequency in multiple cases, the directional edge weight is defined as the number of corresponding causal relationships, and the weight value of each edge is determined based on the data in Table 2 and

Table 3. Partial Edge Weighting for a Subset of Links.

Node	N1	N2	N3	N4	N5	N6	N7	N8	N9	N10	…
N1	0	0	0	3	2	0	0	0	0	0	…
N2	0	0	0	0	0	0	0	0	0	0	…
N3	0	0	0	0	0	0	0	5	0	0	…
N4	0	0	0	0	3	0	0	0	0	0	…
…	…	…	…	…	…	…	…	…	…	…	…

. Table 3 and

Table 4. Characteristic Parameter Values of Causal Networks.

Parameter Name	Parameter Values	Parameter Name	Parameter Values
Several (nodes)	112	Network diameter	6
There are several border articles	270	Network density	0.0315
Average	3.57	Average clustering coefficient	0.153
Average weighting	3.3	Average path length	2.13

serve a critical methodological purpose: they make the derivation of edge weights—a fundamental step in constructing the quantitative network model—explicit and verifiable. Displaying excerpts of the adjacency matrix allows readers to scrutinize the data foundation, moving beyond a black-box description of “weights were assigned” to showing exactly how qualitative insights were operationalized into the quantitative parameters ($a_{ij}$) that drive all subsequent network analyses (degree, centrality, propagation models).

The network metrics are computed from the data generated in Gephi, and the resulting characteristic parameter values are reported in Table 4. These complex network metrics enable the assessment of each node’s importance within the network model and provide quantitative support for investigating the risk propagation mechanism of runway incursions.

After calculating and ranking the degree values of all nodes, the main results are shown in Figure 3. The reported out-degree and in-degree values represent the binary count of direct causal connections (based on matrix A), not the sum of edge weights. Among all nodes, N89 (fog with visibility below minimum standards) has the highest out-degree of 18, followed by N13 (misunderstanding of ATC instructions) with an out-degree of 15, and N71 (unreasonable taxi-route design/setting) with an out-degree of 12. This indicates that once these three risks occur, they are likely to trigger other risk factors, ultimately leading to cascading effects and runway incursion events. The high out-degree of these nodes reveals their pivotal role as initiators within the causal network. For instance, N89 directly impairs multiple operational capabilities simultaneously: it reduces visual acquisition of runway/taxiway markings, decreases navigation accuracy, increases controller and pilot workload, heightens communication demands, and complicates conflict detection. This multifaceted impact explains why a single low-visibility condition is statistically linked to the activation of numerous downstream risk factors (e.g., navigation errors, communication breakdowns, procedural deviations). Similar logic applies to N13 and N71, which serve as direct catalysts for chains of human error and system inefficiency, respectively. In addition, N31 (failure to taxi via the assigned route) has the highest in-degree of 14, suggesting that it is driven by multiple upstream risk factors.

The clustering coefficient distribution shown in Figure 4 reveals pronounced heterogeneity in the local aggregation patterns of risk factors within the runway incursion causal network. N1 (ambiguous controller instructions) ranks first with a clustering coefficient of 0.52, indicating a highly interconnected neighborhood structure among its adjacent risk factors. Once such a core risk factor is triggered, the dense interdependencies within its neighborhood can readily facilitate risk transmission and induce domino-like cascading effects. For instance, ambiguous controller instructions may not only directly impair pilot decision-making but also propagate to secondary risks such as vehicle incursions and failures in the airfield lighting system.

In addition, N99 (insufficient night lighting), N59 (substandard lighting in construction areas), and N37 (radio signal interference) are identified as nodes with relatively high clustering coefficients, also exhibiting strong local clustering characteristics. These nodes can function as local “amplifiers” during risk propagation, substantially enlarging the impact scope of an individual risk event. Therefore, runway incursion prevention strategies should prioritize multi-layered mitigation measures targeting these high-clustering key nodes to effectively contain localized cascades and reduce system-wide risk.

Using the TOPSIS method described above, the closeness coefficient of each node is calculated to evaluate node importance. The computed results show that the top ten key nodes, ranked by importance, are listed in

Table 5. Closeness Centrality of Key Nodes in Causal Network Models.

Node	Proximity	Risk Factors
N31	0.872	Failure to taxi via the assigned route
N1	0.865	Ambiguous controller instructions
N76	0.851	Imperfect low-visibility operating procedures (LVO)
N99	0.843	Insufficient night lighting
N10	0.832	Excessive controller workload
N45	0.821	Unreasonable alarm threshold settings
N26	0.815	Failure to use taxi guidance lights
N37	0.809	Radio signal interference
N63	0.798	Lack of multi-department joint exercises/drills

.

Through the calculation, the initial load and the capacity of the nodes of 112 nodes in the complex network caused by runway incursion are determined, and the comparison of the initial load and capacity of important nodes is screened out as shown in Figure 5.

The computational statistics analyze the capacity, load, and capacity-load ratio of the key nodes, as shown in Figure 6.

The probability of runway incursion into all nodes of the network is calculated, and the probability of risk of key nodes is sorted as shown in Figure 7.

The risk propagation probability of 112 nodes in the network is calculated, and the risk propagation ability and probability of the sorted key nodes are shown in Figure 8.

The figure indicates that N10 (excessive controller workload) and N14 (taxi-route memory error) exhibit relatively high risk propagation probability, implying that these factors are more likely to trigger runway incursion events. In addition, N1 (ambiguous controller instructions) and N99 (insufficient night lighting) show the highest propagation intensity, suggesting broader and stronger cascading impacts once activated. Accordingly, excessive controller workload (N10), taxi-route memory error (N14), ambiguous controller instructions (N1), and insufficient night lighting (N99) are identified as key risk indicators for runway incursions.

4.3. Sensitivity Analysis of the Tolerance Coefficient (β)

To ensure the robustness of the identified key risk nodes is not contingent upon a single empirical value of the parameter β, a sensitivity analysis was performed. The coefficient β was varied systematically from 0.02 to 0.10 in increments of 0.01. For each value, the risk propagation probability Q for each node was recalculated, and the resulting set and ranking of the top ten key nodes were examined.

The results demonstrate that while the absolute Q values for individual nodes fluctuate with β, the core set of the most influential key nodes (notably N1, N10, N14, and N99) consistently remained at the top of the rankings across the entire tested range, with the ranking order itself showing substantial stability. For instance, the composition of the top five key nodes, ranked by Q, remained identical when β was decreased to 0.03 or increased to 0.09. This confirms that the main findings regarding the identity of the critical propagation nodes are not sensitive to the choice of β within a plausible interval. Therefore, the value β = 0.06 is justified as it ensures the model possesses reasonable sensitivity to failure while yielding stable and reliable managerial insights.

5. Conclusions

This study addresses runway incursion risk identification and mechanism interpretation by integrating grounded theory with complex network analysis. A causal network model of runway incursions is established to reveal key risk factors and their interactions. Compared with conventional qualitative summaries or single-factor statistics, the proposed framework models causal couplings among risk factors and characterizes cascading propagation behaviors, enabling a systematic understanding of runway incursion risk. The main findings are summarized as follows:

1.

Construction of a grounded theory-based risk factor system.

Using runway incursion event reports and safety bulletins from the Chinese civil aviation system (2022–2025) as the empirical data, a three-stage grounded theory coding procedure (open coding, axial coding, and selective coding) is applied to extract and categorize risk factors. N structured risk factor system is developed, comprising five main categories (personnel, equipment and facilities, environment and meteorology, information and coordination, and organization and management) and twelve sub-categories, which provides a formal indicator basis for subsequent modeling.

2.

Development of a causal complex network model and identification of key nodes.

Based on complex network theory, a runway incursion causal network consisting of 112 nodes and 270 directed edges is constructed. Node degree centrality, betweenness centrality, and closeness centrality are jointly considered, and TOPSIS is employed to evaluate node importance comprehensively, leading to the identification of critical risk nodes that significantly influence runway incursions.

3.

Quantification of risk propagation using load allocation theory.

Within the causal network framework, a load allocation-based mechanism is introduced to quantify each node’s risk propagation probability and propagation intensity. The results indicate that insufficient night lighting (N99), taxi-route memory errors (N14), ambiguous controller instructions (N1), and excessive controller workload (N20) exhibit prominent propagation probability and intensity, showing strong cascading triggering characteristics. These nodes should therefore be prioritized in mitigation and interruption strategies, and the findings provide a quantitative basis for designing targeted prevention measures.

4.

Derivation of targeted operational recommendations.

To translate the analytical findings into concrete safety interventions, specific measures are proposed corresponding to the key risk nodes:

• For excessive controller workload (N10): Implement dynamic staffing models aligned with traffic complexity and enhance decision-support tools to alleviate cognitive fatigue;
• For ambiguous controller instructions (N1): Enforce phraseology standardization through recurrent training and explore automated speech monitoring for real-time correction;
• For taxi-route memory errors (N14): Accelerate the deployment of advanced surface guidance technology (e.g., stop bars, A-SMGCS) and mandate recurrent familiarization training on airport hotspot charts;
• For insufficient night lighting (N99): Establish a rigorous inspection and maintenance regime for airfield lighting, ensuring adherence to standards, particularly in construction areas.

These targeted recommendations aim to provide actionable guidance for airport operators, air navigation service providers, and regulators, thereby strengthening the practical application of the proposed risk assessment framework.