Abstract: In political, economic and social networks, using the allocation rules in cooperative game theory, such as Shapley value and Banzhaf value, to measure the centrality or importance of nodes is an important method to identify key nodes in networks. By considering the different roles of the hyperlinks representing various organizations in hypernetworks, we first generalize the position value to general allocation rule, called υ-position value, in hypernetwork games. The υ-position value can measure the centrality and relative importance of players in hypernetworks, which can be regarded as a generalization of the degree measure in networks. Secondly, we show that the like-Shapley-position value in hypernetwork games can be uniquely characterized by the component hyperlink power and the local balance hyperlink contribution. Finally, we give an example to illustrate application of the υ-position value in the centrality of hypernetworks.

Key words: hypergraph, centrality measure game, cooperative, allocation rule, Position value

摘要： 利用合作博弈理论的分配规则如Shapley值、Banzhaf值等来度量政治、经济和社会网络中节点的中心性或者重要性是识别网络中关键节点的一类重要方法。考虑到在超网络中代表各类组织的超边在网络中发挥的作用不同,本文研究了超网络博弈上一类广义Position值的分配规则,被称为υ-position值。它可以作为网络中度值测度的一类推广,以此来度量网络中参与者的中心性和相对重要性。其次,证明了超网络结构上类Shapley-position值可由分支超边指数和局部平衡超边贡献两个性质所唯一刻画。最后, 举例分析了υ-position值在超网络中心性测度中的应用。

关键词: 超图, 中心度测度, 合作博弈, 分配规则, Position值