## 2 Interdependent Network Construction
### Control-Flight Conflict Interdependent Network  
According to the logical relationship between the flight conflict network and the control network in the actual operation, the control-flight conflict interdependent network is constructed as follows: let \(G1\) and \(G2\) correspond to the flight conflict network and the control network, respectively, then the set of the multi-layer network is \(g=\{G1,G2\}\), and the set of dependency edges is \(C=\{E_{12}\}\). As shown in Figure 6.  
In the actual operation process, the controller is responsible for the control command of the aircraft in the sector, and also for the transfer of control to the aircraft in the adjacent sector and the monitoring task. For the controller, the process of transferring control is usually about 2 min before the aircraft in the adjacent sector enters the sector, and the controller needs to communicate with the aircraft to prepare for the transfer of control. Therefore, the construction of the dependent edge is that the control nodes in the control network are connected to the aircraft nodes in the sector. It is also connected to the nodes of the aircraft in the adjacent sector that are eligible for the transfer of control and to the nodes of the aircraft in the adjacent sector that are in conflict with the nodes of the aircraft in this sector, forming the dependent edge. There is no specific regulation on the communication before the transfer of control rights in ATC. Therefore, in this paper, it is set that when an aircraft is flying to this sector at 600 km/h, the controller needs to communicate 2 min in advance. In other words, the aircraft has to communicate about 20 km before arriving at the sector boundary, and make arrangements for possible conflicts.  
Figure 5: Control network. (**a**) Control sector. (**b**) Control nodes and edges. In Figure (**a**), we draw out 9 square sectors, where the numbers 1–9 indicate the designations of the 9 control sectors.In Figure (**b**), the numbers 1–9 indicate the nodes corresponding to the controllers of the 9 sectors, and the connecting lines between the numbers indicate the presence of connected edges.  
Figure 6: Interdependent network model.  
Therefore, the control node and the adjacent sector aircraft node form a dependent edge when the following conditions are met.  
1. The aircraft node's heading points to the control sector corresponding to the control node.
2. The distance of the aircraft node from the sector boundary is less than 20 km.  
The weights of the dependent edges are also different because of the different tasks and the attributes of the aircraft itself. In the actual control command process, for the controller to command the conflicting aircraft requires more effort than commanding the non-conflicting aircraft; control command of aircraft within the sector will also require more effort than monitoring the aircraft in the adjacent sector. Therefore, in this paper, the node intensity is treated as the edge power of the dependent edge. Equation (3) is used for calculating the edge power of the dependent edge.  
\[w_{ij}=q_{i} \tag{3}\]  
where \(w_{ij}\) denotes the edge right of the contiguous edge between the control node \(j\) and the aircraft node \(i\).  
In this case, it is important to note that the control node is not only connected to the aircraft nodes in its control sector, but also to the aircraft nodes that are about to enter its control sector. The latter node can be judged by the two conditions given in the above section.