## 3 Weighted Local-World Evolution Model
### Rule 2: Edge increase rule  
The topology evolution analysis is applied when adding information/data interchange between equipment entities that make up SIN, including enabling connections between different equipment entities (e.g., enabling data/information exchange between certain equipment entities according to requirements, etc. ), and enabling the connection between a ground control station and an equipment entity. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number** & **Name** & **Number** & **Name** \\ \hline Rule 1 & Node increase rule & Rule 5 & Edge weight evolution rule \\ Rule 2 & Edge increase rule & Rule 6 & Node deletion rule \\ Rule 3 & Local-World construction rule & Rule 7 & Edge delete rule \\ Rule 4 & Bidirectional selection rule & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: SIN Topology Evolution Rules. **Rule 3: Local-world construction rule**  
When a new node is added, the node will be connected with the local network node, which involves the construction of the local-world. Combined with the structure of SIN, a newly added node \(v_{i}\) is first connected in the corresponding layer domain before it is connected across the domain, and it also selects the neighbor node \(v_{j}\) to connect. Symbol \(\Omega\) represents the local-world, symbol \(V_{Set}\) represents the set of nodes connected to the new node \(v_{i}\), and symbol \(V_{SubSet}\) represents the set of nodes connected to the same layer domain of the new node \(v_{i}\). \[\Omega=V_{Set}\cap V_{SubSet} \tag{7}\]  
**Rule 4: Bidirectional selection rule**  
When a new node is added, if two nodes want to establish a connection, then after a node \(v_{i}\) sends a connection request to another node \(v_{j}\) and waits for another node to identify, a valid connection is established between the two nodes. Therefore, it is necessary to establish a bidirectional preferred selection rule. Meanwhile, it is important to not only consider the connections within the local-world, but to also consider the connections outside the local-world. In the local-world, a node \(v_{i}\) is randomly selected as one side of the newly added edge, and the other endpoint performs a two-way preferential selection according to the probability \(p_{a}\). \[p_{a}=\prod\
olimits_{i,j\in local}(i\to j)=\frac{s_{j}}{\sum\
olimits_{k\in local }s_{k}-s_{i}} \tag{8}\]  
Outside the local-world, a node in the local-world is selected as the end of the new edge according to the probability of \(p_{b}\). \[p_{b}=\prod\
olimits_{i\in local}=\frac{s_{i}}{\sum\
olimits_{k\in local}s_{k}} \tag{9}\]  
Then, according to the probability of \(p_{c}\), the other side of the new edge is selected outside the local-world, that is, the probability of selecting a node with a large intensity is larger. \[p_{c}=\prod\
olimits_{j\in local-world}=\frac{s_{j}}{\sum\
olimits_{k\in local -world}s_{k}} \tag{10}\]  
In order to facilitate the later calculation, this paper only considers the circumstances of the two-way merit selection in the case of deletion of the internal edges of the local-world. Therefore, in the local-world, a node \(v_{i}\) is randomly selected as the end of the edge to be eliminated, and the other end is chosen in the local-world according to the probability of \(p_{d}\). \[p_{d}=1-\prod\
olimits_{j\in local}=1-\frac{s_{j}}{\sum\
olimits_{k\in local }s_{k}} \tag{11}\]  
**Rule 5: Edge weight evolution rule**  
After adding edges, a weight \(\omega_{0}\) is added to each newly added edge \(e_{i}\), and for ease of calculation, it is assumed that the newly added edge will only partially cause the weights adjustment of the connection node \(v_{i}\) and its neighbor node \(v_{j}\). There is an evolutionary rule  
\[\omega_{ij}\rightarrow\omega_{ij}+\Delta\omega_{ij} \tag{12}\]  
where, \(\Delta\omega_{ij}=\alpha_{i}\frac{\omega_{ij}}{s_{i}}\), and each time a new edge \(e_{i}\) is introduced, additional traffic \(\alpha_{i}\) will be brought to node \(v_{i}\).