## 1 Introduction  
There are various complex systems in the fields of natural science and social science, such as atmospheric systems, computer networks, and human societies [1; 2; 3; 4]. In these complex systems, there are numerous system factors, which are interrelated and work together on the operating state or output result of the system. However, there is no doubt that among all these factors, there are often a few that play a dominant role, which we call the key influencing factors [5; 6]. In complex systems constrained by multiple factors, it is very important to identify the key influencing factors for mastering the evolution and development law of the system and for obtaining scientific decision-making suggestions or schemes [7]. In fact, to identify the key influencing factors in a complex system, we need deep knowledge and understanding of the system itself. On one hand, it requires long-term observation of the system; on the other hand, it requires the use of advanced technologies and methods to conduct scientific analysis of the system. The existing relevant methods include factor analysis [8], principal component analysis (PCA) [9], regression analysis [10], and so on. Among them, factor analysis is a qualitative analysis method based on the knowledge and experience of the analyst. Compared with the quantitative analysis method based on data, this method is more subject to subjective factors. Principal component analysis (PCA) is designed to find new variables that are linear functions of those in the original dataset. Finding such new variables, the principal components (PCs), requires solving an eigenvalue/eigenvector problem, which is often not feasible when there are too many variables in the dataset. Regression analysis is used to establish a regression model, obtain the model parameters according to the measured dataset, and express the relationship between variables via a mathematical analytic formula. When there is a large number of variables to be studied, this analytical formula is difficult or even impossible to solve. Therefore, although the above methods are widely used in the identification of key influencing factors, they are all targeted at cases with fewer variables. For example, the literature [11; 12; 13] used PCA or regression analysis to identify key influencing factors in different scenarios, and the datasets used only contained 5, 10, and 15 variables, respectively. The experimental simulation method and DEMATEL method are considered the two main methods used to identify the key factors influencing complex systems [14; 15; 16], but each has its own shortcomings, which will be discussed in detail in Section 2. Complex networks abstract things graphically, which can help us understand complex systems from the perspective of the topology of interacting networks [17]. Causal inference, as a science in which the main goal is to discover causal relationships behind variables/things, is essential for rigorous decision making in the study of complex systems [18; 19; 20; 21]. The above two methods draw on the formal methods of graph theory by using nodes and edges to describe variables and the relationship between variables, respectively. The deep integration of these two theories and methods helps to carry out more scientific and in-depth research on complex systems and other problems. When modelling complex systems, we can combine the ideas and methods of complex networks and causal network construction to draw the \"real\" structure of the organization. In network analysis, quantitative indicators such as the degree, degree distribution, and agglomeration coefficient of complex networks can be used for heuristic calculation of causal effects. When studying the dynamic characteristics of the network, the topological structure and causal transfer structure of the network can be considered at the same time to provide a scientific basis for the decision making of complex systems.