基于非回溯矩阵中心性的超图可靠性研究  

Study on the reliability of hypergraphs based on non-backtracking matrix centrality

作　　者：彭浩[1,2] 钱程 赵丹丹[1] 钟鸣 韩建民[1] 谢紫伊 王伟 PENG Hao;QIAN Cheng;ZHAO Dandan;ZHONG Ming;HAN Jianmin;XIE Ziyi;WANG Wei(School of Computer Science and Technology,Zhejiang Normal University,Jinhua 321004,China;Key Laboratory of Intelligent Educational Technology and Application,Zhejiang Normal University,Jinhua 321004,China;College of Public Health,Chongqing Medical University,Chongqing 400016,China)

机构地区：[1]浙江师范大学计算机与科学技术学院,浙江金华321004 [2]浙江师范大学浙江省智能教育技术与应用重点实验室,浙江金华321004 [3]重庆医科大学公共卫生学院,重庆400016

出　　处：《网络与信息安全学报》2024年第1期22-32,共11页Chinese Journal of Network and Information Security

基　　金：国家自然科学基金(62074212,61902359,61702148);信息网络安全公安部重点实验室开放课题(C20607);重庆医科大学未来青年医学创新计划(W0150)。

摘　　要：近年来,超图作为网络科学的一个研究热点,引起了广泛的关注。超图区别于传统图的结构特点在于它的超边可以同时连接多个节点,从而形成更为复杂和高阶的关系。在这样的网络结构中,有效地识别重要的节点和超边成为一个关键的挑战。特征向量中心性是一个常见的度量标准,但当网络中存在着极大度值的枢纽节点时,使用特征向量中心性度量方法会使结果表现出局域性,限制了该方法的应用场景。因此,将超图转化成对应的线图,在此基础上使用非回溯矩阵中心性这一方法,该方法在评估超边重要性时表现出更好的均匀性和区分度。此外,还探讨了特征向量中心性和非回溯矩阵中心性在超图中节点重要性评估上的应用。通过比较这两种方法,研究发现非回溯矩阵中心性在区分节点重要程度方面具有更明显的优势。研究不仅包括理论分析和模型构建,还包括对真实世界数据的实证。为了验证所提方法和结论,选取了6个真实世界超图作为实验对象。通过在这些超图上的应用,证明了非回溯矩阵中心性在识别重要节点和超边方面的有效性。研究为超图中关键元素的识别提供了一种新的视角和方法,对于理解和分析实际复杂网络系统,具有重要的理论和实践意义。In recent years,there has been widespread attention on hypergraphs as a research hotspot in network science.The unique structure of hypergraphs,which differs from traditional graphs,is characterized by hyperedges that can connect multiple nodes simultaneously,resulting in more complex and higher-order relationships.Effectively identifying important nodes and hyperedges in such network structures poses a key challenge.Eigenvector centrality,a common metric,has limitations in its application due to its locality when dealing with hub nodes with extremely high degree values in the network.To address this issue,the hypergraphs were transformed into their corresponding line graphs,and non-backtracking matrix centrality was employed as a method to measure the importance of hyperedges.This approach demonstrated better uniformity and differentiation in assessing the importance of hyperedges.Furthermore,the application of both eigenvector centrality and non-backtracking matrix centrality in assessing the importance of nodes in hypergraphs was explored.Comparative analysis revealed that non-backtracking matrix centrality effectively distinguished the importance of nodes.This research encompassed theoretical analysis,model construction,and empirical studies on real-world data.To validate the proposed method and conclusion,six real-world hypergraphs were selected as experimental subjects.The application of these methods to these hypergraphs confirmed the effectiveness of non-backtracking matrix centrality in identifying important nodes and hyperedges.The findings of this research offer a fresh perspective and approach for identifying key elements in hypergraphs,holding significant theoretical and practical implications for understanding and analyzing complex network systems.

关 键 词：超图 特征向量中心性 非回溯矩阵中心性 向量中心性 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]