## 2 Related Work
### SIN Dynamic Topology Model
#### 2.2.2 Directed and Weighted Edge  
Through analysis, we can see that the connection between nodes is different during the transmission of data, information, and instructions. Therefore, taking \(E=\{e_{1},\;e_{2},\;\ldots,e_{m}\}\) (edge set) indicates the link between various types of nodes. There are two situations that need to be discussed separately. **Situation 1 (about direction). ** For example, if node \(V_{Int}\) is mainly responsible for the collection of intelligence information, the connection between node \(V_{Int}\) and other nodes \(V_{Other}\) mainly has two situations. One situation is to distribute data/information to other nodes \(V_{Other}\), and establish an information output connection (\(e_{out}\)), and the other situation is to receive instruction information from the command and control node \(V_{CC}\) and establish an information input connection (\(e_{in}\)). These two situations above are different in direction, so the transfer direction must be considered in the analysis of the data information transmission. Therefore, it is necessary to define directed edges and undirected the edges. **Situation 2 (about weight). ** For example, if node \(V_{Inf\_Pro}\) is mainly responsible for space information processing, there are also two main situations of connection between the node \(V_{Inf\_Pro}\) and other nodes. One situation is to accept a large amount of data/information from different nodes, and the other is to feedback data/information processing results to relevant nodes. In comparison, since the received data is the original raw data/information collected by each node and processed unprocessed, the amount of data in this part of the data information is large, and the processed data/information is fed back. Therefore, it is relatively lightweight data/information. The weights of the edges involved in the above two are different. It is necessary to define the edges in this case by weight values. Therefore, considering the relationship, direction, and weight between nodes \(V_{u}\) and \(V_{v}\), the ternary mathematics representation of the directed and weighted edge is given as follows:  
\[E=<R(u,v),D(u,v),W(u,v)> \tag{3}\]  
where, symbol \(R\) means the relationship between nodes \(V_{u}\) and \(V_{v}\), including raw data/information transmission, post-processing information transmission, instruction transmission, and other connection relationships. Symbol \(D\) represents whether or not there is a direction between nodes \(V_{u}\) and \(V_{v}\), and \(D(u,v)\in(0,1)\). Symbol \(W\) stands for the weight of the connection between nodes \(V_{u}\) and \(V_{v}\), and \(W(u,v)\in(0,1)\). For the direction problems mentioned above, make the following provisions: when \(D(u,v)=1\), it indicates that there is a direction from node \(V_{u}\) to \(V_{v}\), that is, \(e_{1}=(u,v)\) and \(e_{2}=(v,u)\) are not equal, and when \(D(u,v)=0\), it indicates that there is no direction from node \(V_{u}\) to \(V_{v}\), that is, \(e_{1}=(u,v)\) and \(e_{2}=(v,u)\) are equal. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Node Properties (Divided by Function)**} \\ \hline
1 & reconnaissance nodes & navigation nodes & communication nodes &... \\ \hline
2 & space information acquisition nodes & space information processing nodes & control nodes &... \\ \hline
3 & communication & investigation & intelligence & navigation and & missile warning & battlefield situational \\  & broadcast nodes & monitoring nodes & detection nodes & positioning nodes & nodes & awareness nodes &... \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Node Division. For the weight issues mentioned above, and combining the relationships between nodes, we can define the weight between nodes \(V_{u}\) and \(V_{v}\) with \(W_{uv}\), and a network of size \(N\times N\) can be represented by the connection weight \((W_{uv})_{N\times N}\), where \(u=1,2,\ldots,N,\ v=1,2,\ldots,N\).