Abstract: It is of great practical value to identify the vital nodes in the network for studying the topology and functional characteristics of the network. The topology of hypernetwork based on hypergraph is hypergraph. Because the hyperedges in hypergraph can contain any number of nodes, the hypernetwork can clearly express the complex relationship of multi-dimension, multi-criteria. In order to better mine the vital nodes in the hypernetwork, based on the theory and properties of hypergraph, this paper proposes the adjacency structure entropy of hypergraph to identify the vital nodes in the hypernetwork. By studying the relationship between the nodes and their direct and indirect nodes, this method uses the node information entropy to describe the importance of different nodes in the hypernetwork. The advantage of this algorithm is that it not only considers the properties of the nodes in the hypernetwork, but also integrates the influence of neighbor nodes. Moreover, because this algorithm only uses the local attributes of nodes, its complexity is low. And through the empirical analysis of the research cooperation hypernetwork, the results show that the adjacency structure entropy can accurately and effectively identify the vital nodes in the hypernetwork, which provides a certain reference for the future research on the vital nodes in the hypernetwork and the topological structure of the hypernetwork.

Key words: hypergraph, hypernetwork, vital node, network structure entropy, adjacency structure entropy

摘要： 识别网络中的关键节点对研究网络的拓扑结构及功能特性具有重要的实际应用价值。基于超图的超网络拓扑结构为超图，由于超图中的超边可以包含任意数量的节点，使得超网络能够清晰明了地表达出多元、多维、多准则的复杂关系。为了更好地挖掘超网络中的关键节点，基于超图理论及性质，提出超图中的邻接结构熵识别超网络中的关键节点，该方法通过研究节点及其直接与间接节点间的关系，利用节点信息熵刻画不同节点在超网络中的重要性。其优势在于不仅考虑了超网络中节点自身的性质，也融合了邻居节点的影响力，且由于该算法只利用节点的局部属性，故其复杂度较低。并通过对科研合作超网络进行的实证分析，结果表明邻接结构熵能够准确有效地识别超网络中的关键节点，为今后研究超网络中的关键节点以及研究超网络的拓扑结构提供一定的借鉴和参考。

关键词: 超图, 超网络, 关键节点, 网络结构熵, 邻接结构熵