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Structural centrality in fuzzy social networks based on fuzzy hypergraph theory
Computational and Mathematical Organization Theory ( IF 1.8 ) Pub Date : 2020-06-27 , DOI: 10.1007/s10588-020-09312-x
Qian Wang , Zeng-Tai Gong

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.

中文翻译:

基于模糊超图理论的模糊社会网络的结构中心

众所周知,关键网络成员的知识对于模糊社交网络分析至关重要。迄今为止,大多数旨在确定关键成员的研究都已采取网络结构中心性措施。由于模糊图不能有效地描述模糊社交网络的节点之间的多维关系,因此开发了一种基于模糊超图数学理论的模糊社交网络模型,从而可以更直观,更直观地表示模糊社交网络。模糊社会网络的模糊超图模型是指一个结构,顶点集作为一个对象集,模糊关系结构中的模糊关系由隶属函数和模糊关系矩阵表示。利用模糊社交网络的模糊超图模型,给出了结构中心性的定义(即,度中心性,相对度中心性,亲密性中心,相对亲密性中心,中间性中心和相对中间性中心)。最后,通过实例分析,阐述了利用模糊超图建立模糊社会网络的过程和集中度的计算方法。
更新日期:2020-06-27
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