计算机科学

计算机科学 ›› 2025, Vol. 52 ›› Issue (12): 92-101.doi: 10.11896/jsjkx.241000090

• 数据库&大数据&数据科学 • 上一篇    下一篇

基于层加权和重力中心性的多层网络重要节点识别

王建波1,2,4, 罗雨1, 许小可3, 杜占玮2, 李平1   

  1. 1 西南石油大学计算机与软件学院 成都 610500
    2 香港大学公共卫生学院 香港 999077
    3 北京师范大学计算传播研究中心与新闻与传播学院 北京 100875
    4 四川警察学院智慧警务与国家安全风险治理重点实验室 四川 泸州 646000
  • 收稿日期:2024-10-18 修回日期:2025-02-15 出版日期:2025-12-15 发布日期:2025-12-09
  • 通讯作者: 王建波(jianbow2021@gmail.com)
  • 基金资助:
    深港澳科技计划项目(C类项目)(SGDX20230821091559022);国家自然科学基金(62173065);北京市自然科学基金(4242040);智慧警务与国家安全风险治理重点实验室2025年度开放课题一般项目(ZHKFYB2503);智慧警务与国家安全风险治理重点实验室2024年度开放课题重点项目(ZHKFZD2401)

Identifying Influential Nodes in Multilayer Networks Based on Layer Weighting and Gravity Centrality

WANG Jianbo1,2,4, LUO Yu1, XU Xiaoke3, DU Zhanwei2, LI Ping1   

  1. 1 School of Computer Science and Software Engineering, Southwest Petroleum University, Chengdu 610500, China
    2 School of Public Health, The University of Hong Kong, Hong Kong 999077, China
    3 Computational Communication Research Center and the School of Journalism and Communication, Beijing Normal University, Beijing 100875, China
    4 Key Laboratory of Intelligent Policing and National Security Risk Management, Sichuan Police College, Luzhou, Sichuan 646000, China
  • Received:2024-10-18 Revised:2025-02-15 Published:2025-12-15 Online:2025-12-09
  • About author:WANG Jianbo,born in 1980,Ph.D,lecturer,master’s supervisor.His main research interests include network science(complex networks),machine learning and deep learning algorithms and applications,and big data analysis.
  • Supported by:
    This work was supported by the Shenzhen-Hong Kong-Macau Science and Technology Project(Category C)(SGDX20230821091559022),National Natural Science Foundation of China(62173065),Natural Science Foundation of Beijing(4242040),Intelligent Policing and National Security Risk Management Laboratory Open Topics for the Year 2025(ZHKFYB2503) and Intelligent Policing and National Security Risk Ma-nagement Laboratory Open Topics for the Year 2024(ZHKFZD2401).

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摘要： 识别多层网络中的重要节点是网络科学中的一个研究热点,对于理解网络的结构和功能起着至关重要的作用。受引力模型启发,现有大多数方法主要基于局部或全局拓扑结构信息,忽略了多层网络的层内和层间结构对节点的影响,限制了节点识别的最终性能。对此,提出了一种基于层加权和重力中心性算法来识别多层网络的重要节点。首先,该算法结合网络的层内和层间结构赋予每层网络权重,以此量化度中心性在不同层的影响力。其次,考虑网络的层间结构对传播路径的影响,进而定义节点之间的有效距离。最后,根据引力公式获得节点在整个网络中的影响力值。在9个真实网络上的多个实验表明,所提算法与6种具有代表性的方法相比,具有较高的准确率和分辨率。

关键词: 影响力节点, 引力模型, 中心性, 层权重, 多层网络

Abstract: Identifying key nodes in multilayer networks is a major research focus in network science,as it plays a crucial role in understanding network structure and function.Inspired by the gravity model,most existing methods primarily rely on local or global topological information,often overlook the influence of intra-layer and inter-layer structures on nodes in multilayer networks.This oversight limits the effectiveness of node identification.To address this,this paper introduces a layer weighting and gravity centrality algorithm for identifying key nodes in multilayer networks.The algorithm first assigns weights to each network layer by considering both intra-layer and inter-layer structures,thus quantifying the influence of degree centrality across different layers.Next,it incorporates the impact of inter-layer structures on propagation paths to define the effective distance between nodes.Finally,the influence of each node within the entire network is calculated using a gravity-based formula.Extensive experiments on nine real-world networks show that the proposed algorithm offers higher accuracy and resolution compared to six benchmark methods.

Key words: Influential node, Gravity model, Centrality, Layer-weighted, Multilayer network

中图分类号: 

  • TP391
[1]ZHANG Y,WANG X,YU J,et al.Adaboosting graph attention recurrent network:A deep learning framework for traffic speed forecasting in dynamic transportation networks with spatial-temporal dependencies [J].Engineering Applications of Artificial Intelligence,2024,127:107297.
[2]ZAREIE A,SHEIKHAHMADI A,JALILI M,et al.Finding influential nodes in social networks based on neighborhood correlation coefficient [J].Knowledge-Based Systems,2020,194:105580.
[3]MASOUDI-SOBHANZADEH Y,GHOLAMINEJAD A,GHEISARI Y,et al.Discovering driver nodes in chronic kidney disease-related networks using Trader as a newly developed algorithm [J].Computers in Biology and Medicine,2022,148:105892.
[4]MOWERS M,MIGNONE B K,STEINBERG D C.Quantifying value and representing competitiveness of electricity system technologies in economic models [J].Applied Energy,2023,329:120132.
[5]WU X,WU X,WANG C Y,et al.Synchronization in multiplex networks [J].Physics Reports,2024,1060:1-54.
[6]HU M,LI J,CAI C,et al.Software defined multicast for large-scale multi-layer leo satellite networks [J].IEEE Transactions on Network and Service Management,2022,19(3):2119-2130.
[7]FAN Z,WU X,MAO B,et al.Output discernibility of topological variations in linear dynamical networks [J].IEEE Transactions on Automatic Control,2024,69(8):5524-5530.
[8]TAN Q,ZHANG F,WANG T,et al.Social Network User Influence Evaluation Algorithm Integrating Structure Centrality [J].Computer Science,2021,48(7):124-129.
[9]SALAVATI C,ABDOLLAHPOURI A,MANBARI Z.Ranking nodes in complex networks based on local structure and improving closeness centrality [J].Neurocomputing,2019,336:36-45.
[10]NEWMAN M E J.A measure of betweenness centrality based on random walks [J].Social Networks,2005,27(1):39-54.
[11]NEGRE C F A,MORZAN U N,HENDRICKSON H P,et al.Eigenvector centrality for characterization of protein allosteric pathways [C]//Proceedings of the National Academy of Sciences.2018:E12201-E12208.
[12]ZHANG P,WANG T,YAN J.PageRank centrality and algorithms for weighted,directed networks [J].Physica A:Statistical Mechanics and Its Applications,2022,586:126438.
[13]LI Z,REN T,MA X,et al.Identifying influential spreaders by gravity model [J].Scientific Reports,2019,9(1):8387.
[14]LIU F,WANG Z,DENG Y.GMM:A generalized mechanicsmodel for identifying the importance of nodes in complex networks [J].Knowledge-Based Systems,2020,193:105464.
[15]SHANG Q,DENG Y,CHEONG K H.Identifying influential nodes in complex networks:Effective distance gravity model [J].Information Sciences,2021,577:162-179.
[16]ZHANG Q,SHUAI B,LYU M.A novel method to identify influential nodes in complex networks based on gravity centrality [J].Information Sciences,2022,618:98-117.
[17]HAJARATHAIAH K,ENDURI M K,ANAMALAMUDI S,et al.Algorithms for finding influential people with mixed centrality in social networks [J].Arabian Journal for Science and Engineering,2023,48(8):10417-10428.
[18]CHAKRABORTY T,NARAYANAM R.Cross-layer betweenness centrality in multiplex networks with applications[C]//2016 IEEE 32nd International Conference on Data Engineering(ICDE).IEEE,2016:397-408.
[19]SOLÁ L,ROMANCE M,CRIADO R,et al.Eigenvector centra-lity of nodes in multiplex networks [J].Chaos:An Interdisciplinary Journal of Nonlinear Science,2013,23(3):033131.
[20]BERGERMANN K,STOLL M.Fast computation of matrixfunction-based centrality measures for layer-coupled multiplex networks [J].Physical Review E,2022,105(3):034305.
[21]LI Z,TANG J,ZHAO C,et al.Improved centrality measure based on the adapted PageRank algorithm for urban transportation multiplex networks [J].Chaos,Solitons & Fractals,2023,167:112998.
[22]DE DOMENICO M,SOLÈ-RIBALTA A,OMODEI E,et al.Ranking in interconnected multilayer networks reveals versatile nodes [J].Nature Communications,2015,6(1):6868.
[23]BASARAS P,IOSIFIDIS G,KATSAROS D,et al.Identifying influential spreaders in complex multilayer networks:A centrality perspective [J].IEEE Transactions on Network Science and Engineering,2017,6(1):31-45.
[24]ZHOU X,BOUYER A,MALEKI M,et al.Identifying top influential spreaders based on the influence weight of layers in multiplex networks [J].Chaos,Solitons & Fractals,2023,173:113769.
[25]LYU L,ZHANG K,BARDOU D,et al.A new centrality measure based on random walks for multilayer networks under the framework of tensor computation [J].Physica A:Statistical Mechanics and Its Applications,2019,526:121000.
[26]WAN L,ZHANG M,LI X,et al.Identification of importantnodes in multilayer heterogeneous networks incorporating multirelational information [J].IEEE Transactions on Computational Social Systems,2022,9(6):1715-1724.
[27]DE DOMENICO M,LANCICHINETTI A,ARENAS A,et al.Identifying modular flows on multilayer networks reveals highly overlapping organization in interconnected systems [J].Physical Review X,2015,5(1):011027.
[28]DE DOMENICO M,SOLÈ-RIBALTA A,COZZO E,et al.Mathe-matical formulation of multilayer networks [J].Physical Review X,2013,3(4):041022.
[29]DE DOMENICO M,SOLÈ-RIBALTA A,GÓMEZ S,et al.Navigability of interconnected networks under random failures [C]//Proceedings of the National Academy of Sciences.2014:8351-8356.
[30]LI M,ZHANG Q,DENG Y.Evidential identification of influential nodes in network of networks [J].Chaos,Solitons & Fractals,2018,117:283-296.
[31]RANI S,KUMAR M.Influential Node Detection and Rankingwith Fusion of Heterogeneous Social Media Information [J].IEEE Transactions on Computational Social Systems,2022,10(4):1852-1874.
[32]NI C,YANG J,PANG Z,et al.Seeding strategy based on weighted gravity centrality in multiplex networks[J].IEEE Transactions on Network Science and Engineering,2022,10(1):331-345.
[33]NI C,YANG J.Two-step seeding strategy in multiplex net-works with inter-layer conversion cost of influence [J].Chaos:An Interdisciplinary Journal of Nonlinear Science,2022,32(8):083135.
[34]LYU L,ZHANG T,HU P,et al.An improved gravity centrality for finding important nodes in multi-layer networks based on multi-PageRank [J].Expert Systems with Applications,2024,238:122171.
[35]NIWATTANAKUL S,SINGTHONGCHAI J,NAENUDORNE,et al.Using of Jaccard coefficient for keywords similarity[C]//Proceedings of the International Multiconference of Engineers and Computer Scientists.IMECS,2013:380-384.
[36]LIU X,YE S,FIUMARA G,et al.Influential spreaders identification in complex networks with topsis and k-shell decomposition [J].IEEE Transactions on Computational Social Systems,2022,10(1):347-361.
[37]GAUTHIER T D.Detecting trends using Spearman’s rank correlation coefficient [J].Environmental Forensics,2001,2(4):359-362.
[38]AI J,HE T,SU Z,et al.Identifying influential nodes in complex networks based on spreading probability [J].Chaos,Solitons & Fractals,2022,164:112627.
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