## 3 System Model Design
### Calculating Mobile Similarity of Node and Narrowing the Node Range by a Single Threshold
#### 3.2.1 Computation of the Mobile between Nodes  
**A: Calculating mobile similarity by the number of neighbor nodes**  
The closer the social relationships between nodes in the network, the greater the chance that they will meet later. The neighbor nodes are relative to the transmission distance or the number of transmission hops. We judge the moving similarity of the nodes by the number of common neighbor nodes between the nodes. As shown in Figure 2, after a time \(\Delta t\), the node \(u\) and the node \(v\) move from the left side of Figure 2 to other positions, and the neighbor nodes included are different, and the number of neighbor nodes is also different. Node \(u\) and node \(v\) contain a common neighbor node. Figure 1: Information collection and update between mobile nodes in the networks. After time \(\Delta t\), the number of common neighbor nodes and neighbor nodes is different. The left side is the communication range of time \(t_{1}\) node \(u\) and node \(v\), and the right side is the communication range of time \(t_{2}\) node \(u\) and node \(v\). The similarity between nodes is related to the number of common neighbor nodes. When there are more common neighbor nodes between two nodes, the closer the relationship between the two nodes is, the higher the similarity between the two nodes is. Therefore, when the node is at rest, the similarity between the nodes calculated by the number of neighbor nodes can be calculated by the number of common neighbor nodes accounting for the total number of neighbor nodes:  
\[N\_similaritystatic(node_{u},node_{v})=\frac{[Q_{u}\cap Q_{v}]}{[Q_{u}\cup Q _{v}]} \tag{5}\]  
where the static similarity of node \(u\) and node \(v\) is calculated, \(Q_{u}\) represents the neighbor node of node \(u\), \(Q_{v}\) represents the neighbor node of node. The mobile similarity of neighbor nodes is also related to the number of corresponding neighbor nodes. After the elapse of time A, if the number of co-neighbor nodes between nodes increases, the similarity between nodes increases. Conversely, when the common neighbor nodes are less than before, the similarity is reduced. Therefore, we can use Equation (6) as the calculation of node moving similarity:  
\[N\_similarity_{moving}(node_{u},node_{v})=\frac{[(Q^{\prime}u\cap Q^{\prime}v)- (Q_{u}\cap Q_{v})]}{[(Q^{\prime}u\cap Q^{\prime}v)]} \tag{6}\]  
where \(Q^{\prime}u\) represents the neighbor node after the time \(u\) passes the time \(\Delta t\), and \(Q^{\prime}v\) represents the neighbor node after the time \(\Delta t\) of the node \(v\). The combination of static node similarity and dynamic node similarity is collectively referred to as node moving similarity, denoted as \(N\_similarity\). \[N\_similarity=\alpha\bullet N\_similarity_{static}+\beta\bullet N\_similarity_{moving} \tag{7}\]  
where \(\alpha\) and \(\beta\) are correlation coefficients of node similarity and \(\alpha+\beta=1\). **B: Calculating the mobile similarity of a node by its historical movement trajectory**  
The position of the moving track of the node and its moving state are collected at the time of information collection, which aims to judge the moving similarity of the moving track by calculating  
Figure 2: The physical change of the degree of mobile similarity between mobile nodes. the similarity of the moving track during a period of time. In general, the more similar the movement trajectory of two nodes in the network, the higher the success rate of message forwarding. Therefore, we will use the time of node trajectory motion and its communication area to work together. During the node information collection process, we collect the movement trajectory state \(m\_track_{node}\) of the node, which contains the set of motion positions of the node and the set of movement states at time \(t\). At the same time, we use this information as input to calculate the mobile similarity of the node. First, in the real scene, the state of the nodes may be different in different periods.