(1). Node Similarity

We believe that the closer the social relationship is, the more likely it is to meet in the future. We first consider the number of shared neighbor nodes in the node's social relationship. The similarity between nodes is defined as the number of common neighbors between two nodes. This equation can be defined as: 

$$sim\_{ij} = \frac{|\mathcal{C}\_i \cap \mathcal{C}\_j|}{|\mathcal{C}\_i \cup \mathcal{C}\_j|} \tag{2}$$

where *simij* represents the similarity between node *i* and node *j*. |··· | represents the number of nodes in the collection. *Ci* is the set of neighbor nodes connected to node *i* at the current time, and *Cj* is the set of neighbor nodes connected to node *j* at the current time. Considering that two nodes share a similar set of neighbor nodes, two nodes are more likely to pass data through a common neighbor. Therefore, we consider that the relationship between the two nodes is higher and the probability of data transmission is higher.

### (2). Devices' Mobility

Considering other factors that affect the value of total social relationships, node mobility change and node connection transformation are important factors that must be considered in the value of the overall social relationship. In a mobile opportunistic network, since the nodes are constantly moving, the connection between the nodes and the neighbors will change over time. In a continuous *T* time interval, the degree of change in the movement of such a node relative to another node is defined as the degree of motion transformation:

$$\text{Move}\_{i\bar{j}} = \frac{\left| \left( \mathbf{C}\_i' \cup \mathbf{C}\_j' \right) \cup \left( \mathbf{C}\_i \cup \mathbf{C}\_j \right) \right| - \left| \left( \mathbf{C}\_i' \cup \mathbf{C}\_j' \right) \cap \left( \mathbf{C}\_i \cup \mathbf{C}\_j \right) \right|}{\left| \left( \mathbf{C}\_i' \cup \mathbf{C}\_j' \right) \cup \left( \mathbf{C}\_i \cup \mathbf{C}\_j \right) \right|} \tag{3}$$

where *Moveij* is the moving degree of the node at the current time. *C i* represents the set of neighbor nodes of node *i* before the *T* time interval, as is the case with *C j* . *Ci* represents the set of neighbor nodes of node *i* at the current time, and the same is true for *Cj*. From Equation (3), we can deduce that the higher the frequency of the movement of node *j* relative to node *i*, the larger the transformation of its neighbor node set relative to *i*, and the greater the degree of motion transformation.

### (3). Connection Transformation

The degree to which a shared neighbor node of a node's connection with respect to another node changes and the dynamics of the neighbor node connection between them are referred to as the connection degrees of transition. In successive *T* time intervals, the degree of change in the connection of such a node relative to another node is defined as the connection transformation:

$$\text{Com}\_{ij} = \frac{\left| \left( \mathbf{C}'\_i \cap \mathbf{C}'\_j \right) \cup \left( \mathbf{C}\_i \cap \mathbf{C}\_j \right) \right| - \left| \left( \mathbf{C}'\_i \cap \mathbf{C}'\_j \right) \cap \left( \mathbf{C}\_i \cap \mathbf{C}\_j \right) \right|}{\left| \left( \mathbf{C}'\_i \cap \mathbf{C}'\_j \right) \cup \left( \mathbf{C}\_i \cap \mathbf{C}\_j \right) \right|} \tag{4}$$

From the formula (4), *Connij* is the degree of change in the shared neighbor node set connected to the node. It can be seen that the greater the change in the set of shared neighbor nodes of the connection is, the higher the value of *Connij*. By observing and analyzing the common neighbor nodes of the two nodes, we can see the motion changes of the two nodes in the current network. When the common neighbor node with node *i* associated with node *j* increases, the connection probability between node *i* and node *j* will increase, and then the possibility of data exchange will be improved.

Through the analysis of node similarity and node relative change, we can quantify the social relationship values between two nodes as follows:

$$S\_{ij} = a \dot{s} m\_{ij} + \beta (1 - Move\_{ij}) + \gamma (1 - Comn\_{ij}) \tag{5}$$

Among them, the smaller the degree of transformation, the greater the value of social relations. *α*, *β*, *γ* are the coefficients of node similarity, moving transform, and connection transform, respectively. They represent the weighting factors that influence the value of social relationships by different factors, and *α* + *β* + *γ* = 1.
