Contribution Analysis for Assessing Node Importance Indices with Principal Component Analysis
HU Gang1, XU Xiang2, ZHANG Wei-ming2, ZHOU Yun2
1. School of Management Science and Engineering, Anhui University of Technology, Maanshan, Anhui 243032, China;
2. Science and Technology on Information Systems Engineering Laboratory, National University of Defense Technology, Changsha, Hunan 410073, China
Abstract：In network theory,it is interest to study the influences of different nodes on the key nodes in the network,and build or select the proper node importance index to model it.This paper selects seven node importance indices to calculate and analyze their contributions in nodes' importance evaluation with Principal Component Analysis.Seven empirical networks are used for experiments.Moreover,the order of different contributions of indices is obtained,and the correlation analysis between the most important index and the other indices is carried out using the Kendall coefficient,and factors affecting the correlation coefficient are also discussed.This paper provides a way to select the node importance index in the network,and the results could also be used for studying the relationships between different nodes.
[1] Bonacich P.Factoring and weighting approaches to status scores and clique identification[J].Journal of Mathematical Sociology,1972,2(1):113-120.
[2] Freeman L C.A set of measures of centrality based on betweenness[J].Sociometry,1977,40(1):35-41.
[3] Freeman L C.Centrality in social networks conceptual clarification[J].Social Networks,1979,1(3):215-239.
[4] Kleinberg J M.Authoritative sources in a hyperlinked environment[J].Journal of Acm,1999,46(5):604-632.
[5] Qi X,Duval R D,Christensen K,et al.Terrorist networks,network energy and node removal:a new measure of centrality based on laplacian energy[J].Social Networking,2013,2(1):19-31.
[6] Burt R S.Structural Holes:The Social Structure of Competition[M].Harvard University Press,2010.
[7] Chen D B,Lü L,Shang M S,et al.Identifying influential nodes in complex networks[J].Physica A Statistical Mechanics & Its Applications,2012,391(1):1777-1787.
[8] Phillip Bonacich.Factoring and weighting approaches to status scores and clique identification[J].Journal of Mathematical Sociology,1972,2(1):113-120.
[9] Dangalchev C.Residual closeness in networks[J].Physica A Statistical Mechanics & Its Applications,2006,365(2):556-564.
[10] Kitsak M,Gallos L K,Havlin S,et al.Identification of influential spreaders in complex networks[J].Nature Physics,2011,6(11):888-893.
[11] Brin S,Page L.The anatomy of a large-scale hypertextual Web search engine[A].International Conference on World Wide Web[C].Elsevier Science Publishers B.V.1998.107-117.
[12] Poulin R,Boily M C,Msse B R.Dynamical systems to define centrality in social networks[J].Social Networks,2000,22(3):187-220.
[13] Linyuan L,Zhang Y C,Ho Y C,et al.Leaders in social networks,the delicious case[J].Plos One,2011,6(6):e21202.
[14] 汪应洛.系统工程.第5版[M].北京:机械工业出版社,2015.52-55. Wang Ying-luo.Systems Engineering.Fifth Edition[M].Beijing:China Machine Press,2015.52-55.(in Chinese)
[15] 汪小帆,李翔,陈关荣.网络科学导论[M].北京:高等教育出版社,2012.161-162. Wang Xiao-fan,Li Xiang,Chen Guan-rong.An Introduction of Network Science[M].Beijing:Higher Education Press,2012.161-162.(in Chinese)
[16] Klovdahl A S.Social networks and the spread of infectious diseases:the AIDS example[J].Social Science & Medicine,1985,21(11):1203-1216.
[17] 刘忠华,于华,杨方廷.基于复杂网络理论的水网节点重要性评价研究[J].中国科学:技术科学,2014(12):1280-1294. Liu Zhong-hua,Yu Hua,Yang Fang-ting.Evaluate the node importance for water network based on complex network theory[J].Chinese Science:Technical Science,2014(12):1280-1294.(in Chinese)
[18] 王政,孙锦程,刘晓强,等.基于复杂网络理论的大型换热网络节点重要性评价[J].化工进展,2017,36(5):1581-1588. Wang Zheng,Sun Jin-cheng,Liu Xiao-qiang,Jiang Ying,Jia Xiaoping,Wang Fang.Evaluation of the node importance for large heat exchanger network based on complex network theory[J].Chemical Industry and Engineering Progress,2017,36(5):1581-1588.(in Chinese)
[19] 韩忠明,吴杨,谭旭升,等.面向结构洞的复杂网络关键节点排序[J].物理学报,2015,64(5):421-429. Han Zhong-ming,Wu Yang,Tan Xu-sheng,Duan Da-gao,Yang Wei-jie.Ranking key nodes in complex networks by considering structural holes[J].Acta Physica Sinica,2015,64(5):421-429.(in Chinese)
[20] 苏晓萍,宋玉蓉.利用邻域"结构洞"寻找社会网络中最具影响力节点[J].物理学报,2015,64(2):1-11. Su Xiao-ping,Song Yu-rong.Leveraging neighborhood "structural holes" to identifying key spreaders in social networks[J].Acta Physica Sinica,2015,64(2):1-11.(in Chinese)
[21] Yu H,Cao X,Liu Z,et al.Identifying key nodes based on improved structural holes in complex networks[J].Physica A Statistical Mechanics & Its Applications,2017,486.
[22] 于会,刘尊,李勇军.基于多属性决策的复杂网络节点重要性综合评价方法[J].物理学报,2013,62(2):020204-1-020204-9. Yu Hui,Liu Zun,Li Yong-jun.Key nodes in complex networks identified by multi-attribute decision-making method[J].Acta Physica Sinica,2013,62(2):020204-1-020204-9.(in Chinese)
[23] Zhang K,Zhang H,Wu Y D,et al.Evaluating the importance of nodes in complex networks based on principal component analysis and grey relational analysis[A].IEEE International Conference on Networks[C].2011.6955(2):231-235.
[24] Kendall M G.The treatment of ties in ranking problems[J].Biometrika,1945,33(3):239-251.
2019, Vol. 47 
