Structural centrality in fuzzy social networks based on fuzzy hypergraph theory

Abstract

The knowledge of key network members is generally known to be critical to fuzzy social network analysis. Thus far, most studies aiming to identify critical members have taken network structural centrality measures. Since fuzzy graph cannot effectively depict the multidimensional relationships between the nodes of fuzzy social networks, a fuzzy social network model is developed complying with a mathematical theory of fuzzy hypergraph, allowing fuzzy social network to be represented more intuitively and visually. A fuzzy hypergraph model of fuzzy social network refers to a structure, vertex set acts as an object set, and the fuzzy relation in fuzzy relation structure is expressed by membership function and fuzzy relation matrix. With the fuzzy hypergraph model of fuzzy social networks, the definitions of structural centrality are given (i.e., degree centrality, relative degree centrality, closeness centrality, relative closeness centrality, betweenness centrality and relative betweenness centrality). Lastly, by analyzing examples, the process of building fuzzy social network with fuzzy hypergraph and the calculation method of centrality are illustrated.