Abstract: It is a basic and challenging task to identify important nodes in hypernetworks, and the related research is of great value for further analysis of network topology and functional characteristics. In order to break through the limitations of the existing important node recognition methods, an important node recognition method based on node propagation entropy is proposed by using hypergraph and information entropy theory. This method takes into account both local and global topology information of nodes, uses the node clustering coefficient and the number of neighbors to represent the local propagation influence of node information, the global influence of the node information is reflected by the shortest path between nodes and K-shell centrality, and fully considers the influence of nodes and their neighbors, the importance of nodes in the network is represented by the size of node propagation entropy finally. Using monotonicity, robustness and SIR propagation model evaluation criteria, compared with other methods on six real networks from different fields, experimental results show that the proposed method can identify the important nodes in the hypernetwork accurately and effectively.

Key words: hypergraph, hypernetwork, important node, node propagation entropy

摘要： 超网络中识别重要节点是一项基础且具有挑战性的重要课题，相关研究对进一步分析网络拓扑结构和功能特性具有广泛的应用价值。为了突破已有的重要节点识别方法评估的局限性，利用超图及信息熵理论，提出一种基于节点传播熵的超网络重要节点识别方法。该方法兼顾节点的局部和全局拓扑信息，利用节点聚集系数和邻居数目表征节点信息的局部传播影响，通过节点间最短路径和K壳中心性反映节点信息的全局传播影响，充分考虑节点自身及其邻域节点的影响，最终利用节点传播熵来表征节点在网络中的重要性。并通过单调性、鲁棒性以及SIR传播模型评价标准，在六个来自不同领域的真实网络上与其他方法进行比较，实验结果表明，该方法能够准确有效地识别网络中的重要节点。

关键词: 超图, 超网络, 重要节点, 节点传播熵