**1. Introduction**

With the mobile cellular network evolving to the fifth generation, huge amounts of information data are generated every day. Opportunistic complex social networks have become a common data delivery platform [1–3], and the popularity of mobile devices has enabled a variety of new services in social networks to be realized [4]. Many social tools, such as Google Plus [5], Facebook [6], and Twitter [7], have a large number of users and generate data in each moment. The traditional social network approaches to dealing with transmission and reception of big data diversification faces challenges due to the diversification of online data. Many wireless devices used to deliver information and then faced data overload, which would be a hindrance to information interworking and information sharing. In order to cope with the data transmission in 5G wireless networks, we need to design a model and more convenient transmission mode to implement data forwarding in a flexible manner, which is more suitable for complex network environments.

In opportunistic social networks, there is no complete end-to-end path between most mobile devices, so nodes communicate by hop by hop. One common method of data dissemination is a base station (BS) that can first deliver a message to a mobile device. The device of the user could carry the message and transmit it to other mobile devices via Device-to-Device(D2D) communication. The mobile device receives data and waits for an "opportunity" to deliver the message to the next mobile device [8]. For data forwarding problems, most existing work either assumes that users are completely unselfish, i.e., they are willing to help any user to pass information [9,10], or assume that users are absolutely selfish and that users need to be encouraged to participate in data transmission [11,12]. However, in real-life scenarios, users are not absolutely selfish or absolutely selfless. Their level of selfishness may be random or related to social relationships. Therefore, we have established a cooperative relationship to solve this problem.

However, the social network is a complex network. The challenge is it is hard to estimate the daily data sent and received by users [13,14]. It is difficult to satisfy a large amount of data decision, transmission, and storage by a personal PDA device alone. It may cause a low delivery ratio and an excessive energy consumption of the transmission device. The decision could be made by assistance devices, such as the base station or the edge. The delivery ratio can be improved and data transmission energy consumption can be reduced. In addition, this network is divided into multiple disconnected subnets due to the loss of nodes due to problems, such as device movement, failure, or non-cooperation [15,16]. Such nodes are called critical nodes. The loss of key nodes will cause the network to be disconnected, which leads to the loss of important data in the network [17,18]. The researcher proposed the concept of probabilistic routing [19]. Each node maintains a link probability table that reaches any other node in the network, and then it could determine the key nodes of message transmission by comparing probability sizes. However, this method is too simple to calculate probabilistic values in the case of an explosion of information. It is also too much trouble to perform calculations and decisions every time the data transmission node performs. Even the task of maintaining a routing table is too expensive. Therefore, we collected and used the node's encounter data, cooperation information, node characteristics, and social relationship to assist decision-making to predict key nodes in the opportunistic social network, and propose a relatively simple transmission model based on probability prediction.

To solve the huge amount of information in the 5G network, the mobile device has too much energy consumption for decision-making, transmission, and storage of a large amount of data. We propose ways to assist decision-making information transmission by devices, such as base stations or edges. Since the opportunistic complex social network does not necessarily acquire information about all nodes in the entire network, the node information is incomplete and the characteristics of each node cannot be utilized more fully to filter the key nodes. Therefore, the collected network information may not be complete, and the resulting encounter probability matrix may be incomplete or even sparse. In response to this problem, we first calculated some node social relationship values, cooperation probability values, and node encounter probabilities by pre-processing some data collected over a period of time. Then, we establish three related feature matrices and the vector of residual energy of nodes, and propose an algorithm based on hybrid probability matrix decomposition to predict key nodes. Finally, we filter the key nodes more reasonably and effectively through the impact of the collected feature information on the message passing between nodes in the network. Specifically, hidden information between nodes can also be fully utilized through the model to maximize the value of the node. By adaptive message forwarding decisions, the purpose of selecting a relay node and improving network resource utilization is achieved.

Specifically, the main contribution of this paper can be summarized as the following three aspects:


to form a hybrid model to predict the encounter cooperation (EC) values between nodes, and filter the key encounter nodes through EC values.

3. We have designed a simpler way to transfer information to share the large number of transmission tasks of the central equipment. The mobile device only needs to request the central node to encounter the probability table of the other node and the destination node. Then, according to the information in the table, the data is passed to the neighbor node that has a higher value than its own and the destination node. The simulation results show that the PNEC algorithm has excellent effects in the message transmission process between nodes, and maximizes the characteristics of mobile nodes in the network.
