**2. Related Work**

In the form of 5G networks, base station construction is relatively dense. The base station needs to collect the soaring data generated by devices, and analyze, process and transmit the data further. As shown in [20], a practical system architecture is proposed to process and extract useful information, and through the data caching mechanism, to solve the user data requirements. This approach increases the complexity of data processing. In such cases, most of the work of data transmission and data sharing can be done by the mobile device. The node's transmission decision, calculation, and other tasks can be assigned to the base station or edge equipment to reduce the node energy consumption. Many researchers have proposed ways for mobile devices to deliver messages in opportunistic mobile complex social networks. In such a network, there is no guarantee that the full connection path between the source and destination exists at any time, which makes the traditional routing protocol unable to deliver messages better between nodes. Some researchers have proposed probabilistic routing protocols for the network [19]. The nodes predict the reachability probability between the nodes by storing their encounter information, and select the nodes with higher encounter probability as the relay node. Such a method will increase the energy consumption of nodes in the case of the heavy task of 5G network data transmission.

In mobile social networks, some researchers have proposed using community structure to make data forwarding decisions. They assume that people in the same community would have closer relationships and more opportunities to connect with each other. The concept of the probability of the source node to the destination node is proposed by tracking the encounter situations of the nodes to study the activity of the node and the probability of reaching the target node, using the Poisson model of the social network contact. On this basis, the contact-aware opportunity-based forwarding (CAOF) scheme [21] is proposed by calculating the global and local probability of two different transmission phases. It includes the forwarding scheme between the inter-community transmission phase and the intra-community transmission phase. In the inter-community phase, neighbor nodes with higher global activity and high probability of source node to target node are selected as relays. Furthermore, forwarding decisions are determined by local metrics in the internal phase of the community. In this program, social characteristics and cooperation relationships may not be considered for integration into the design of the scheme, and may not perform well when the nodes are selfish.

In addition, there is an interesting study on mobile social networks. Since the mobile social network consists of nodes with different social attributes, the connection is transmitted or shared by chance. Some researchers have proposed a routing algorithm based on social identity awareness (SIaOR) [22]. They believe that many socially aware routing algorithms ignore an important social attribute, social identity. Therefore, researchers propose an opportunity routing algorithm in mobile social networks by considering the social identity and social impact of mobile nodes in mobile social networks. The algorithm not only considers the multiple social identities of mobile nodes, but also their social impacts. However, it is difficult to measure the ability of nodes to forward data if they simply consider the social identity impact with the target node. Moreover, nodes with strong social relationships may not be suitable nodes for cooperation.

A new sensing method is the Internet of Things in the Mobile Crowd Sensor Network (MCSN). There are two existing transmission mechanisms: One is to transmit data through a cellular network, the other is an opportunistic transmission method through short-range wireless communication technology. Some researchers have proposed that the cost of cellular network transmission is high and it is not conducive to increasing user participation. Therefore, researchers focus on the application of wireless communication technology in MCSN by constructing a new opportunistic propagation model. They proposed an opportunistic data transmission mechanism based on the Socialization Susceptible Infected Susceptible Epidemic Model (SSIS) [23]. The mechanism uses the SSIS model to obtain a social relationship table by analyzing the social relationships of mobile nodes. The source node that performs the sensing task through the combination of the social relationship table and the spray and wait mechanism selectively propagates the data to other nodes until it reaches the destination node that can send the data to the platform. Using the spray and wait method will make the transmission mode more complicated and the node energy consumption increase.

Some researchers have proposed a new mobile opportunistic network routing protocol, MLProph [24], through machine learning and through further research on the mobile social network. The model uses decision trees and neural networks to train various factors, such as the predicted value inherited from the PROPHET routing scheme, node popularity, node's power consumption, speed, and location, to further calculate the probability of successful delivery of information. The algorithm trains based on historical information to obtain an equation for calculating the probability to detect whether the node can send the message to the destination node. This is an interesting way to make probabilistic predictions through machine learning methods, however, this method may only consider the nodes themselves, without considering the characteristics between the nodes.

According to the discussion on those methods, there is no complicated decision-making scheme considering the cooperative relationship and social relationship of the nodes. Additionally, the key neighbors are calculated and decided by nodes. When the amount of data transmission is large, calculation and decision by nodes may increase energy consumption. We need more complicated decision-making methods to solve data transmission problems more conveniently when the amount of data skyrockets in 5G networks. A good and effective decision-making mode determines whether the information transmission between mobile devices can achieve the desired effect. Many researchers have proposed a probabilistic routing method to calculate the probability of a nodes' final successful delivery to the destination by training the probabilistic equation. However, these methods could not consider whether the selected relay node is willing to cooperate in forwarding messages. Furthermore, nodes move randomly and socially, and it is worth considering whether such social relations will affect the activity rules of nodes. Therefore, we designed a model based on probabilistic prediction by quantifying social relationships and cooperative relationship values. We need to analyze and process and make decisions on a large amount of data, and improve the user satisfaction through active caching of edge devices to meet the needs of users in the 5G network [20]. In this case, we can make transmission calculations and decisions through small base stations or edge devices to reduce the workload of mobile nodes. Consequently, we have collected the characteristic information of nodes in the region through the base station and quantified the collected information to form the encounter matrix, cooperative matrix, and social relation matrix, respectively. Then, we used the improved probability matrix decomposition method to integrate the matrix information to update the encounter probability matrix and predict the probability value of the encounter and cooperation between two nodes without the encounter history information and updated the existing value. Finally, the neighbor node is filtered by the size of EC in the updated probability matrix. Experiments show that the proposed model reduces the network overhead of non-cooperative nodes, optimizes the path of messages to the destination nodes, and enables messages to be transmitted along the cooperative nodes with a high probability of encountering the destination nodes.

### **3. Model Design**

### *3.1. Node Data Collection and Transmission*

The base station (BS) collects information of all nodes in the area and trains the encounter matrix at period, T, in the area. As shown in Figure 1, the base station collects the information of all nodes in the region over a period of time and trains the final probability matrix according to the designed model through these features. If the social relationship and the cooperative relationship cannot be obtained in the initial stage of the model application, the final probability matrix is the historical encounter probability matrix. When a node has a transmission task, the probability table of known nodes and destination nodes is requested from the base station. Specifically, when a new node enters the area, its characteristic information is sent to the BS. If it carries a probability forecast table, the BS obtains the table and updates its own matrix based on the probability forecast table obtained from the BS. If it does not carry a probability forecast table, it is sent to the matrix trained by the BS in the area. After the T period, the BS trains the matrix, M, according to Algorithm 1 (refer to Section 3.5), and transmits the matrix information according to the node information collected in the past T periods. During the period, the matrix, M, is updated by Algorithm 2 (refer to Section 3.5) according to the obtained node's probability forecast table and communication between BS before the T period. The main update idea is to add a record without some node information. The exchange of information when the mobile devices meet is also the same as updating the records carried. The message carried by the mobile devices is sent to the encounter devices whose probability of encounter is greater than the mobile device's own and destination mobile device's probability of encounter. If there is no record of the destination node, it is sent to nodes in the encounter node that have a higher probability of encountering mobile devices in another area.

**Figure 1.** Example diagram of node information exchange in the area.

### *3.2. Encounter Probability and Social Relationship Decomposition*

### 3.2.1. Encounter Relationship Value Calculation

First, we give a definition of computing the encounter probability. To facilitate the description of related problems, in this paper, *mij* is the probability of an encounter between node *i* and node *j* over a period of time. That is, the probability that node *i* and node *j* meet within the perceived range. The definition is as follows:

$$\begin{aligned} w\_{ij} &= \frac{w\_{ij}}{\sum\_{\substack{i\\adj}}^n w\_{i,adj}} \end{aligned} \tag{1}$$

where *i* denotes the source node, and *j* denotes the target node. *wij* is the number of historical encounters between node *i* and node *j* within a certain period of time. *wi*,*adj* indicates that the number of times that node *i* has met with other nodes is within a certain period of time.

### 3.2.2. Social Relationship Value Calculation

The number of encounters between nodes simply reflects the node's encounters over a period of time. We cannot just rely on the number of node history encounters to predict an encounter in the future. Here, we consider the quantitative factors of mobile node social relations.
