Social network theory is an important paradigm of social structure research, which has been widely used in various fields of research. This paper reviews the development process and the latest progress of social network theory research and analyzes the research application of social network. In order to reveal the deep social structure, this paper analyzes the structure of social networks from three levels: microlevel, mesolevel, and macrolevel and reveals the origin, development, perfection, and latest achievements of complex network models. The regular graph model, P1 model, P2 model, exponential random graph model, small-world network model, and scale-free network model are introduced. In the end, the research on the social network structure is reviewed, and social support network and social discussion network are introduced, which are two important contents of social network research. At present, the research on social networks has been widely used in coauthor networks, citation networks, mobile social networks, enterprise knowledge management, and individual happiness, but there are few research studies on multilevel structure, dynamic research, complex network research, whole network research, and discussion network research. This provides space for future research on social networks.

Professional athletes' social networks have rarely been explored. In this paper, we propose a framework to analyze athletes' social networks. Based on the characteristics of athletes' social network structure and social support theory, the matrix distribution is introduced to describe the network structure. The observation model of the Bayesian network is established, and then the Gaussian process analysis model of sparse matrix is used to investigated the network. We collected real-world data of athletes' social networks by questionnaires, which contain eight thematic network data. With our method, the interpersonal network of professional athletes is analyzed and the adjacency relationships are predicted. Finally, taking the social subnet of the athlete social network as an example and using the model and algorithm, the node support factor analysis and the complex network community convergence factors are analyzed. We found that professional athletes' social networks have a stronger small-world characteristic than the general public's social networks. The proposed model and algorithm provide a new quantitative approach for studying professional athletes' social networks.INDEX TERMS Bayesian network, matrix distribution, professional athletes, social network.

This paper mainly focus on the hazard materials treatment center location problem using the fuzzy multiobjective programming approach. We consider the factor of treating volume of each treatment center into the classical MAX-MIN model. The problem is formulated as a bi-objective problem, which is rarely studied previously. Additionally, to provide a more realistic model structure, decision makers imprecise aspiration levels for the goals are incorporated into the model through fuzzy modelling approach. In the decision process, a fuzzy goal programming method is developed. We also discuss the computing approach and prove that the fuzzy optimal solution has a good performance.

In response to the lack of research on the online social network structure of athletes, elements of research on the online social network structure of athletes were constructed based on the whole network perspective and through the study of the characteristics of the whole online social network structure of athletes, in order to provide reference for the physical and mental health development of athletes from a new perspective. Data were collected through questionnaires, and several software programs were used to preprocess and analyse the collected data. Through the analysis of the online whole network structure, it was found that the network density of the online support network was generally greater than that of the online discussion network, and athletes still showed stronger practical support demands and behaved more rationally in the process of training and learning life, while from the perspective of the relationship structure, the athletes’ family and classmates’ online support is weaker than that in previous studies; in terms of the whole network, strong relationships still dominate in this population, while attention should be paid to the impact of weak relationships.

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