## 1 Introduction  
With the rapid development of China's economy and aviation technology, China has been adding new airports and planning new routes in recent years. According to the International Air Transport Association (IATA), the total civil passenger traffic within China will surpass that of the United States around 2025, becoming the world's largest aviation market [1]. The resulting contradiction between the rapid growth of air traffic flow and the inadequate development of air traffic management system capacity is becoming more and more serious, which brings enormous pressure and burden to the work of controllers. As the main participant and implementer in the air traffic management process, the controller's work status is the main reason for determining whether the air traffic control (ATC) system can operate smoothly or not. The controller workload, as an important factor affecting the controller's work status, is of great significance to maintaining a reasonable and stable operation of the ATC system, whether its evaluation method is scientific or not. Therefore, this paper intends to study the interrelationship between controllers and aircraft to provide support for controller workload evaluation. In terms of controller workload evaluation, experts from various countries have conducted a lot of research, mainly including subjective and objective evaluation methods. [PERSON] was the first to propose the Air Traffic Workload Input Technique (ATWIT) based on the control interface in 1985 [2], [PERSON] proposed the National Aeronautics and Space Administration-task load index (NASA-TLX) in 1988 [3], and British scientists proposed the \"DORATASK\" method based on controlled work time [4]. With the maturity of related technology, the research on objective evaluation methods is also developing and improving. [PERSON] used principal component analysis to analyze the change pattern of electrocardiogram (ECG) signals with working time and concluded that two ECG indicators, RR mean and SDNN, can evaluate the fatigue state [5]. In 2020, [PERSON] and [PERSON] proposed a method to evaluate the workload using EEG signals [6]. [PERSON] used eye-movement recognition to make a recognition assessment of the controller workload [7]. However, the subjective methods mentioned above have the problems of excessive subjectivity and timeliness, and the objective methods can interfere with the normal work of controllers because of their need to wear measurement equipment. From a cognitive point of view, controllers, as the core of the air traffic system, need to understand the airspace and its situational evolution, including aircraft position and other information, with the help of equipment, and make adjustments in case of unexpected situations. This is also the main cause of the controller's workload. Therefore, [PERSON] proposed a controller workload evaluation system constructed from four indicators, such as traffic density, convergence, dispersion, and sensitivity, by analyzing information such as aircraft position and heading in the airspace [8; 9]. In fact, the essence of the evolutionary development of the air traffic system belongs to the evolution and development of complex relationships between various elements of the system, led by aircraft, and each other. The complex network theory is able to describe the complex system abstractly and emphasize the topological characteristics of the system, which enables the system essentially to be understood. Therefore, the introduction of complex network theory is expected to be able to analyze and understand the system from its essence and make an effective assessment of the air situation and controller workload. Therefore, [PERSON] et al. of the American Board of Aeronautical Radio were the first to introduce complex network theory into the field of air traffic control, using the relevant metrics in complex network theory as indicators for evaluating the measurement of control difficulty and controller workload [10]. [PERSON] et al.