陈如达,杨凡,谢剑,陶自为

• 1:广西科技大学理学院
• 2:广西高校智能计算与分布式信息处理重点实验室(广西科技大学)
• 3:广西科技大学智能信息处理与图计算重点实验室
• 4:广西科技大学计算机科学与技术学院(软件学院)

摘要(Abstract)：

在复杂网络中，对重要节点进行排序可以识别网络中的核心与关键节点，对调控传播过程具有重要意义。目前已有许多关于重要节点排序的研究，但如何高效、全面地利用节点信息提取特征并评估节点重要性，仍需进一步探索。本文结合节点的局部与全局信息，提出一种基于图神经网络（graph neural network, GNN）的重要节点排序方法。首先，利用节点的度、节点间最短距离和k-shell值，捕获节点的局部与全局信息；其次，获取节点信息后，采用图注意力机制聚合邻居节点特征，并学习节点的表示向量；最后，通过全连接层计算节点重要性。本文在真实网络数据集上进行实验，采用单调性指数（monotonicity index, MI）和肯德尔τ系数验证所提方法的有效性。实验结果表明，该模型在不同的网络结构中均能有效地对网络重要节点进行排序。

关键词(KeyWords)： 复杂网络;节点排序;图神经网络(GNN);图注意力机制;节点特征

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金项目（62062010）;; 广西高校中青年教师科研基础能力提升项目（2024KY0360）资助

作者(Author): 陈如达,杨凡,谢剑,陶自为

DOI: 10.16375/j.cnki.cn45-1395/t.2026.03.007

参考文献(References)：

• [1]KITSAK M , GALLOS L K , HAVLIN S , et al.Identification of influential spreaders in complex networks[J].Nature Physics,2010,6(11):888-893.
• [2]CHEN W , LAKSHMANAN L V S , CASTILLO C.Information and influence propagation in social networks[M].San Rafael:Morgan&Claypool Publishers,2013.
• [3]XU M,WU J P,LIU M Q,et al. Discovery of critical nodes in road networks through mining from vehicle trajectories[J]. IEEE Transactions on Intelligent Transportation Systems,2018,20(2):583-593.
• [4]COHEN R,HAVLIN S,BEN-AVRAHAM D. Efficient immunization strategies for computer networks and populations[J]. Physical Review Letters,2003,91(24):247901.
• [5]PASTOR-SATORRAS R,VESPIGNANI A. Immunization of complex networks[J]. Physical Review E,2002,65(3):036104.
• [6]FREEMAN L C. Centrality in social networks:conceptual clarification[J]. Social Network,1979,1(3):215-239.
• [7]ZHANG J H,ZHANG Q S,WU L,et al. Identifying influential nodes in complex networks based on multiple local attributes and information entropy[J]. Entropy,2022,24(2):293.
• [8]L??L Y,ZHOU T,ZHANG Q M,et al. The H-index of a network node and its relation to degree and coreness[J].Nature Communications,2016,7(1):1-7.
• [9]LI Z,REN T,MA X Q,et al. Identifying influential spreaders by gravity model[J]. Scientific Reports,2019,9(1):1-7.
• [10]FENG Y L,WANG H X,CHANG C,et al. Intrinsic correlation with betweenness centrality and distribution of shortest paths[J]. Mathematics,2022,10(14):2521.
• [11]STEPHENSON K,ZELEN M. Rethinking centrality:methods and examples[J]. Social Networks,1989,11(1):1-37.
• [12]BRYAN K,LEISE T. The$25,000,000,000 eigenvector:the linear algebra behind Google[J]. SIAM Review,2006,48(3):569-581.
• [13]周晓燕，曹威，徐超.基于层次时空注意力图卷积的交通速度预测方法[J].广西科技大学学报，2024,35(4):92-99,107.
• [14]黄伟坚，李春贵.基于时空注意力图卷积神经网络的交通速度预测[J].广西科技大学学报，2022,33(1):54-62.
• [15]YU E Y,WANG Y P,FU Y,et al. Identifying critical nodes in complex networks via graph convolutional networks[J]. Knowledge-Based Systems,2020,198:10589.
• [16]ZHAO G H,JIA P,ZHOU A M,et al. InfGCN:identifying influential nodes in complex networks with graph convolutional networks[J]. Neurocomputing,2020,414:18-26.
• [17]OU Y,GUO Q,XING J L,et al. Identification of spreading influence nodes via multi-level structural attributes based on the graph convolutional network[J]. Expert Systems with Applications,2022,203:117515.
• [18]ZHANG M,WANG X J,JIN L,et al. A new approach for evaluating node importance in complex networks via deep learning methods[J]. Neurocomputing,2022,497:13-27.
• [19]XIONG Y,HU Z,SU C,et al. Vital node identification in complex networks based on autoencoder and graph neural network[J]. Applied Soft Computing,2024,163:111895.
• [20]AHMAD W,WANG B,CHEN S. Learning to rank influential nodes in complex networks via convolutional neural networks[J]. Applied Intelligence,2024,54(4):3260-3278.
• [21]FATEMI B,MOLAEI S,PAN S R,et al. GCNFusion:an efficient graph convolutional network based model for information diffusion[J]. Expert Systems with Applications,2022,202:117053.
• [22]KOU J H,JIA P,LIU J Y,et al. Identify influential nodes in social networks with graph multi-head attention regression model[J]. Neurocomputing,2023,530:23-36.
• [23]LU P L,LUO Y,ZHANG T. A critical node identification approach for complex networks combining self-attention and ResNet[J]. International Journal of Modern Physics C:Computational Physics and Physical Computation,2024,35(1):2450014.
• [24]ZHAO X M,YU H T,HUANG R Y,et al. A novel higherorder neural network framework based on motifs attention for identifying critical nodes[J]. Physica A:Statistical Mechanics and its Applications,2023,629:129194.
• [25]QU H B,SONG Y R,LI R Q,et al. GNR:a universal and efficient node ranking model for various tasks based on graph neural networks[J]. Physica A:Statistical Mechanics and its Applications,2023,632:129339.
• [26]席颖，邬学猛，崔晓晖.基于Transformer的节点影响力排序模型[J].计算机科学，2024,51(4):106-116.
• [27]XI Y,CUI X H. Identifying influential nodes in complex networks based on information entropy and relationship strength[J]. Entropy,2023,25(5):754.
• [28]VELI??KOVI??P,CUCURULL G,CASANOVA A,et al.Graph attention networks[J]. arxiv,2017. preprint arxiv:1710.10903.
• [29]MORENO Y,PASTOR-SATORRAS R,VESPIGNANI A.Epidemic outbreaks in complex heterogeneous networks[J].The European Physical Journal B:Condensed Matter and Complex Systems,2002,26(4):521-529.
• [30]KIPF T N,WELLING M. Semi-supervised classification with graph convolutional networks[C]//5th International Conference on Learning Representations,2017.
• [31]HAMILTON W L,YING R,LESKOVEC J. Inductive representation learning on large graphs[C]//31st Annual Conference on Neural Information Processing Systems(NIPS),2017.

文章评论(Comment)：

序号(No.) 时间(Time) 反馈人(User) 邮箱(Email) 标题(Title) 内容(Content)

反馈人(User) 邮箱地址(Email) 反馈标题(Title) 反馈内容(Content)