## 3 Simulation Analysis of Interdependent Networks
### Node Characterization  
As an important tool for analyzing and studying networks, selecting appropriate network characteristic indicators is of great significance for rational analysis of networks. To facilitate a reasonable analysis to quantify the nature of interdependent networks, this paper selects the degree of nodes, node intensity, and weighted clustering coefficients of the network to analyze interdependent networks. 1. Degree. In the interdependent network, the degree of a node is defined as the number of connected edges of the node in the network. Since the interdependent network consists of two layers, the degree of a node includes the inner degree and the outer degree, where the inner degree is the number of connected edges with the node in the same layer of the network, and the outer degree is the number of connected edges with the nodes in the interlayer network. Equation (4) is used to calculate the degree \(k_{i}\) of node \(i\) through the adjacency matrix. \[k_{i}=k_{i1}+k_{i2}=\sum_{V1_{j}\in V1}a_{ij}+\sum_{V2_{j}\in V2}a_{ij} \tag{4}\]  
where \(k_{i1}\) denotes the inner degree of node \(i\), \(k_{i2}\) denotes the outer degree of node \(i\), \(V_{1}\) denotes the set of nodes in the flight conflict network, \(V_{2}\) denotes the set of nodes in the control network, and \(a_{ij}\) denotes the value in row \(i\) and column \(j\) of the adjacency matrix. The higher the degree value of a node, the more it is associated with more aircraft nodes and control nodes in the network, and the greater the degree of its influence on the network. The degree values of each node in the interdependent network are shown in Figure 8.  
As shown in Figure 8, the node degree values of the control nodes are generally much higher than those of the aircraft nodes, which is because controllers need to control all aircraft in their controlled airspace, while pilots, whose main job is to fly the aircraft, only need to have connections with controllers and aircraft that have potential conflicts with themselves. Among the control nodes, node 188 has a higher number of adjacent sectors than node 185, but because it has the highest number of aircraft in its control airspace and the most potential conflicts, its airspace complexity is the highest, its degree value is the highest, and the controller's workload is the highest. 1. Node intensity. The node intensity \(s_{i}\) of a node is the result of weighting the sum of node degree values, which can reflect the number of nodes and their connected nodes in the network, as well as the close relationship between nodes and their connected nodes, and can more clearly describe the importance of nodes in the network. Equation (5) is used to calculate the node intensity \(s_{i}\) of node \(i\). \[s_{i}=\sum_{j=1}^{N}a_{ij}w_{ij} \tag{5}\]  
where \(w_{ij}\) denotes the edge power of node \(i\) and node \(j\), and \(N\) denotes the total number of nodes in the interdependent network. Figure 8: Node degree value. The node intensity of each node in the interdependent network is shown in Figure 9.  
As shown in Figure 9, nodes 3, 28, 58 and 150, and other nodes in the aircraft node node intensity are higher, indicating that the air situation near the node is more complex, and its control node 188 node intensity is also higher, indicating that controllers need to devote more energy to airspace control and conflict deployment, and if their workload is greater, then, at this time, the work strategy should be promptly adjusted and arranged to increase controllers to maintain airspace safety and reduce controller workload. (3) Weighted clustering coefficient. The clustering coefficient is used as an indicator to judge the degree of aggregation of nodes in the network and is the ratio of the actual number of connected edges between a node and all its neighboring nodes to the theoretical number of all connected edges, with the need to consider the edge weights between nodes. Equation 6 is used to calculate the clustering coefficient.