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本文基于有向加权网络模型，构建了三个影响力矩阵，并利用层次分析法对其赋权求和，形成多重影响力矩阵，从而提出了一种基于该矩阵的节点重要性评价方法.该方法通过新定义的交叉强度指标，来表征节点的局部重要性；利用全网节点对待评估节点的重要性影响总值，来表征节点在全网中的相对重要性.在分析影响节点对待评估节点的影响比例时，既考虑到节点间的距离因素，又引入了最短路径条数因素；既考虑了该影响节点对网络中其他节点的影响关系，又考虑了网络中其他节点对该待评估节点的影响关系，使得评价方法更加全面.将算法运用于ARPA网络，结果表明，该方法能有效地区分各节点之间的差异.最后，对实验结果进行连锁故障的仿真对比实验，进一步验证了方法的有效性.In complex networks, the node importance evaluation is of great significance for studying the robustness of network. The existing methods of evaluating the node importance mainly focus on undirected and unweighted networks, which fail to reflect the real scenarios comprehensively and objectively. In this paper, according to the directed and weighted complex network model, by analyzing the local importance of the nodes and the dependencies among all the nodes in the whole network, a new method of evaluating the node importance based on a multiple influence matrix is proposed. Firstly, the method defines the concept of cross strength to characterize the local importance of the nodes. The index not only distinguishes between the in-strength and out-strength of the nodes, but also helps to discriminate the differences in importance among each with an in-degree of 0. In addition, to characterize the global importance of the nodes to be evaluated, we use the total important influence value of all the nodes exerted on the nodes, which makes up the deficiencies of the other evaluation methods which just depend on adjacent nodes. Emphatically, in the analysis of the influence ratio of source node on node to be evaluated, we not only take into account the distance factor between nodes, but also introduce the number of the shortest path factors. In order to make the evaluation algorithm more accurate, according to the number of the shortest paths, we present two perspectives to analyze how other factors affect the influence ratio. One is to evaluate how this source node exerts important influence on the other nodes to be evaluated. The other is to analyze how the other source nodes perform important influence on this node to be evaluated. In view of the above factors, three influence matrices are constructed, including the efficiency matrix, and the other two influence matrices from the perspectives of fixing source nodes and target nodes, respectively. Then, we use analytic hierarchy process to weight the three matrices, thereby obtaining the multiple influence matrix, which makes the global importance evaluation more comprehensive. Finally, the method is applied to typical directed weighted networks. It is found that compared with other methods, our method can effectively distinguish between nodes. Furthermore, we carry out simulation experiments of cascading failure on each method. The simulation results further verify the effectiveness of the proposed method.
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Keywords:
- directed-weighted complex network /
- node importance /
- multiple influence matrix /
- the number of shortest path
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[1] Barabsi A L, Bonabeau E 2003 Sci.Am.28850
[2] LL Y, Chen D B, Ren X L, Zhang Q M, Zhang Y C, Zhou T 2016Phys.Rep. 650 1
[3] Batool K, Niazi M A 2014PLoS One 9 e90283
[4] Zhang Y L, Yang N D, Lall U 2016J.Syst.Sci.Syst.Eng. 25 102
[5] Liu Y H, Jin J Z, Zhang Y, Xu C 2014 J.Supercomput.67723
[6] Han Z M, Wu Y, Tan X S, Duan D G, Yang W J 2015Acta Phys.Sin. 64 058902(in Chinese)[韩忠明, 吴杨, 谭旭升, 段大高, 杨伟杰2015 64 058902]
[7] Li S M, Xu X H 2015Chinese J.Aeronaut. 28 780
[8] Fan W L, Hu P, Liu Z G 2016IET Gener.Transm.Distrib. 10 2027
[9] Liu R R, Jia C X, Zhang J L, Wang B H 2012J.Univ.Shanghai Sci.Technol. 34 235(in Chinese)[刘润然, 贾春晓, 章剑林, 汪秉宏2012上海理工大学学报34 235]
[10] Yu H, Liu Z, Li Y J 2013Acta Phys.Sin. 62 020204(in Chinese)[于会, 刘尊, 李勇军2013 62 020204]
[11] Han Z M, Chen Y, Li M Q, Liu W, Yang W J 2016Acta Phys.Sin. 65 168901(in Chinese)[韩忠明, 陈炎, 李梦琪, 刘雯, 杨伟杰2016 65 168901]
[12] Li J R, Yu L, Zhao J 2014J.UESTC. 43 322(in Chinese)[李静茹, 喻莉, 赵佳2014电子科技大学学报43 322]
[13] Jeong H, Mason S, Barabsi A L 2001Nature 411 41
[14] Freeman L 1977Sociometry 40 35
[15] Kitsak M, Gallos L K, Havlin S, Liljeros F, Muchnik L, Stanley H E, Makse H A 2010Nat.Phys. 6 888
[16] LL Y, Zhang Y C, Yeung C H, Zhou T 2011PLoS One 6 e21202
[17] Brin S, Page L 1998Comput.Net.ISDN Syst. 30 107
[18] Xu J, Li J X, Xu S 2012J.Zhejiang Univ.:Sci.C 13 118
[19] Wang B, Ma R N, Wang G, Chen B 2015J.Comput.Appl. 35 1820(in Chinese)[王班, 马润年, 王刚, 陈波2015计算机应用35 1820]
[20] Zhou X, Zhang F M, Li K W, Hui X B, Wu H S 2012Acta Phys.Sin. 61 050201(in Chinese)[周漩, 张凤鸣, 李克武, 惠晓滨, 吴虎胜2012 61 050201]
[21] Hu P, Fan W L, Mei S W 2015Physica A:Stat.Mech.Appl. 429 169
[22] Fan W L, Liu Z G 2014J.Southwest Jiaotong Univ. 49 337(in Chinese)[范文礼, 刘志刚2014西南交通大学学报49 337]
[23] Kudelka M, Zehnalova S, Horak Z, Kromer P, Snasel V 2015Int.J.Appl.Math.Comput.Sci. 25 281
[24] Thomas J B, Brier M R, Ortega M, Benzinger T L, Ances B M 2015Neurobiol.Aging 36 401
[25] Latora V, Marchiori M 2007New J.Phys. 9 188
[26] Shao F, Cheng B 2014Int.J.Comput.Commun.Cont. 9 602
[27] Griffith D A, Chun Y 2015Netw.Spat.Econ. 15 337
[28] Cai Q S, Liu Y, Niu J W, Sun L M 2015Acta Electron.Sinica. 43 1705(in Chinese)[蔡青松, 刘燕, 牛建伟, 孙利民2015电子学报43 1705]
[29] Zhu Y, Meng Z Y, Kan S Y 1999J.Northern Jiaotong Univ. 23 119(in Chinese)[朱茵, 孟志勇, 阚叔愚1999北方交通大学学报23 119]
[30] Sun S L, Lin J Y, Xie L H, Xiao W D 200722nd IEEE International Symposium on Intelligent Control Singapore, October 1-3, 2007 p7
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