A fuzzy social network centrality analysis model for interpersonal spatial relations

Interpersonal nodes in the social networking sites reflect the para-virtual and para-real relationships, and form a complex social network. To reveal the properties of the interpersonal nodes and their interrelations effectively, this paper develops an evaluation index system, which contains fuzzy comentropy, fuzzy node degree, fuzzy condensation degree, fuzzy cluster coefficient and fuzzy geographic concentration, and particularly proposes a fuzzy social network centrality analysis (FSNCA) model, which combines “node distribution”, “node connection strength” and “node condensation and cluster”, based on the fuzzy graph-theory. The FSNCA model has been successfully applied to study the interpersonal nodes' spatial relations in three social networking services (SNS) cases, in which three progressive layers, “nodes”, “node connections” and “differences between node connections”, are analyzed respectively. In the first case, the “friend group nodes” are studied to evaluate the equilibrium of node distribution in the network space by use of the fuzzy comentropy index. In the second case, the “connections between BBS group regional nodes” are studied to evaluate the centrality status and types of nodes in the network space by use of the fuzzy node degree index. The third case analyzes the “node connections of two kinds of chance relation groups” to evaluate the differences of centrality status in different networks by use of the fuzzy condensation degree, fuzzy cluster coefficient and fuzzy geographic concentration indexes. The systematic cognition of the interpersonal node spatial relations in the SNS community proves that the proposed method can effectively reveal the essence of fuzzy centralities. It sheds some light on the para-virtual and para-real geographical research, which is of significance to enrich the para-virtual and para-real geographical spatial relation theory, and it can also directly support the management and development of social networks of online services.