## 2 Interdependent Network Construction
### Flight Conflict Network  
The flight conflict network in this paper is constructed with aircraft as the network nodes and the relationship between aircraft as the connected edges. The existence of connected edges between the nodes in the network proves that the aircraft represented by the nodes have direct conflict relationships, which will affect the network if not handled in time. Since the conflict relationship is undifferentiated for aircraft, the flight conflict network is an undirected network. In ICAO document 8168, the communication response range between aircraft is defined as 14 n mile, which is about 26 km. Therefore, the following requirements need to be satisfied when constructing the connected edges of the flight conflict network in this paper.  
(1) The positions of the aircraft corresponding to the nodes are in proximity in space, as shown in Figure 1. Aircraft constitute a communication relationship when their distance from each other is less than 26 km.  
(2) Secondary determination of nodes with communication relations. The nodes are judged by the speed barrier method. Since aircraft need to maintain a certain relative interval between each other during operation, an ellipsoidal flight protection zone is constructed for aircraft. The length of the long axis a and short axis b of the flight protection zone is 10 km, and the length z of the polar radius c is 0.3 km, as shown in Figure 2, with reference to the aircraft-related intervals.  
As shown in Figure 3, the flight of two aircraft can be considered as aircraft A at rest and aircraft B flying along the direction of relative motion V. If the direction of relative motion of the aircraft points in the flight protection zone, then when the aircraft maintains the current heading and speed unchanged and the controller does not deploy, eventually the two aircraft will have a conflict. In this case, it is determined that the nodes corresponding to the aircraft constitute a connected edge.  
In Figure 3, VA denotes the direction of velocity of aircraft A; VB denotes the direction of velocity of aircraft B; and V denotes aircraft A and B and the direction of velocity.  
Figure 1: Near position detection area.  
Figure 3: Schematic diagram of speed obstacle model.  
Figure 2: Aircraft flight protected area.  
The set edge power is related to the predicted conflict time existing between the nodes corresponding to the aerials, and the shorter the predicted conflict time, the more urgent the conflict is proved to be, and the larger the edge power is. Equation (1) is used to calculate the edge weight.  
\[\omega_{ij}=\exp(-\frac{L_{0}}{V}) \tag{1}\]  
where \(\omega_{ij}\) denotes the connected edge weight of node \(i\) and node \(j\). \(L_{0}\) is the shortest distance between aircraft B in the direction of velocity \(V\) and the intersection C of the flight protection zone of aircraft A; \(V\) is the relative velocity of the aircraft.  
In the process of control command, if the aircraft in the control sector shows a convergence, then the controller needs to be highly vigilant to make effective control of the aircraft, which will also lead to higher pressure on the controller. On the contrary, if the aircraft shows a discrete attitude, then the controller's pressure will be less. Therefore, in this paper, the control difficulty of controllers by using node intensity response in the flight conflict network. Equation (2) is used to calculate the node intensity.  
\[q_{i}=\sum_{j\in n_{i}}\omega_{ij} \tag{2}\]  
where \(q_{i}\) denotes the node intensity of node \(i\), and \(\omega\) is the set of nodes that form a connected edge with node \(i\).  
As shown in Figure 4, there are six aircraft nodes in the flight conflict network, among which the No. 2 and No. 3 aircraft nodes are in conflict.