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节点中心性指标是从特定角度对网络某一方面的结构特点进行刻画的度量指标, 因此网络拓扑结构的改变会对节点中心性指标的准确性产生重要影响. 本文利用Holme-Kim模型构建可变集聚系数的无标度网络, 然后采用Susceptible-Infective-Removal模型进行传播影响力的仿真实验, 接着分析了节点中心性指标在不同集聚系数的无标度网络中的准确性. 结果表明, 度中心性和介数中心性的准确性在低集聚系数的网络中表现更好, 特征向量中心性则在高集聚类网络中更准确, 而紧密度中心性的准确性受网络集聚系数的变化影响较小. 因此当网络的集聚系数较低时, 可选择度或者介数作为中心性指标进行网络节点影响力评价; 反之则选择紧密度指标或特征向量指标较好, 尤其当网络的集聚系数接近0.6时特征向量的准确性可以高达到0.85, 是度量小规模网络的较优选择. 另一方面, 传播过程的感染率越高, 度指标和介数指标越可靠, 紧密度和特征向量则相反. 最后Autonomous System实证网络的断边重连实验, 进一步验证了网络集聚性的改变会对节点中心性指标的准确性产生重要影响.Measurements of node centrality are based on characterizing the network topology structure in a certain perspective. Changing the network topology structure would affect the accuracy of the measurements. In this paper, we employ the Holme-Kim model to construct scale-free networks with tunable clustering, and consider the four measurements of classical centrality, including degree centrality, closeness centrality, betweenness centrality and the eigenvector centrality. For comparing the accuracy of the four centrality measurements, we simulate the susceptible-infected-recovered (SIR) spreading of the tunable clustering scale free networks. Experimental results show that the degree centrality and the betweenness centrality are more accurate in networks with lower clustering, while the eigenvector centrality performs well in high clustering networks, and the accuracy of the closeness centrality keeps stable in networks with variable clustering. In addition, the accuracy of the degree centrality and the betweenness centrality are more reliable in the spreading process at the high infectious rates than that of the eigenvector centrality and the closeness centrality. Furthermore, we also use the reconnected autonomous system networks to validate the performance of the four classical centrality measurements with varying cluster. Results show that the accuracy of the degree centrality declines slowly when the clustering of real reconnected networks increases from 0.3 to 0.6, and the accuracy of the closeness centrality has a tiny fluctuation when the clustering of real reconnected networks varies. The betweenness centrality is more accurate in networks with lower clustering, while the eigenvector centrality performs well in high clustering networks, which is the same as in the tunable clustering scale free networks. According to the spreading experiments in the artificial and real networks, we conclude that the network clustering structure affects the accuracy of the node centrality, and suggest that when evaluating the node influence, we can choose the degree centrality in the low clustering networks, while the eigenvector centrality and the closeness centrality are still in the high clustering networks. When considering the spreading dynamics, the accuracy of the eigenvector centrality and the closeness centrality is high, but the accuracy of the degree centrality and the betweenness centrality is more reliable in the spreading process at high infectious rates. This work would be helpful for deeply understanding of the node centrality measurements in complex networks.
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Keywords:
- network science /
- node centrality /
- network structure /
- clustering coefficient
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[37] Kendall M G 1938 Biometrika 30 81
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[1] Albert R, Barabsi A L 2002 Rev. Mod. Phys. 74 47
[2] Newman M E J 2003 SIAM. Rev. 45 167
[3] L L, Medo M, Yeung C H, Zhang Y C, Zhang Z K, Zhou T 2012 Phys. Rep. 519 1
[4] Gao Z K, Zhang X W, Jin N D, Norbert M, Jvrgen K 2013 Phys. Rev. E 88 032910
[5] Rong Z H, Tang M, Wang X F, Wu Z X, Yan G, Zhou T 2012 Journal of Electronic Science and Technology 34 801 (in Chinese) [荣智海, 唐明, 汪小帆, 吴枝喜, 严钢, 周涛 2012 电子科技大学学报 34 801]
[6] Aral S, Walker D 2012 Science 6092 337
[7] Zhao J, Yu L, Li J R, Zhou P 2015 Chin. Phys. B 24 058904
[8] Newman M E J 2010 Networks An Introduction(New York: Oxford University Press) p168
[9] Liu J G, Ren Z M, Guo Q, Wang B H 2013 Acta Phys. Sin. 62 178901 (in Chinese) [刘建国, 任卓明, 郭强, 汪秉宏 2013 62 178901]
[10] Ren X L, L L Y 2014 Sci. Bull. 13 4 (in Chinese) [任晓龙, 吕琳媛 2014 科学通报 13 4]
[11] Song B, Jiang G P, Song Y R, Xia L L 2015 Chin. Phys. B 24 100101
[12] Sabidussi G 1966 Psychometrika 31 581
[13] Goh K I, Oh E, Kahng B, Kim D 2003 Phys. Rev. E 67 017101
[14] Borgatti S P 2005 Soc. Networks 27 55
[15] Kitsak M, Gallos L K, Havlin S, Liljeros F, Muchnik L, Stanley H E, Makse H A 2010 Nat. Phys. 6 888
[16] Ren Z M, Shao F, Liu J G, Guo Q, Wang B H 2013 Acta Phys. Sin. 62 128901 (in Chinese) [任卓明, 邵凤, 刘建国, 郭强, 汪秉宏 2013 62 128901]
[17] Chen D, Lv L, Shang M S, Zhang Y C, Zhou T 2012 Physica A 391 1777
[18] Wang J R, Wang J P, He Z, Xu H T 2015 Chin. Phys. B 24 060101
[19] Zhang J, Xu X K, Li P, Zhang K, Small M 2011 Chaos 21 016107
[20] Comin C H, Costa Lda F 2011 Phys. Rev. E 84 056105
[21] Poulin R, Boily M C, Masse B R 2000 Soc. Networks 22 187
[22] Ren Z M, Liu J G, Shao F, Hu Z L, Guo Q 2013 Acta Phys. Sin. 62 108902 (in Chinese) [任卓明, 刘建国, 邵凤, 胡兆龙, 郭强 2013 62 108902]
[23] Garas A, Schweitzer F, Havlin S 2012 New J. Phys. 14 083030
[24] Zeng A, Zhang C J 2013 Phys. Lett. A 377 1031
[25] Travenolo B A N, Costa Lda F 2008 Phys. Lett. A 373 89
[26] Chen D B, Xiao R, Zeng A, Zhang Y C 2013 EPL 104 68006
[27] Lv L, Zhang Y C, Yeung C H, Zhou T 2011 PloS one 6 e21202
[28] Ren Z M, Zeng A, Chen D B, Liao H, Liu J G 2014 EPL 106 48005
[29] Watts D J, Strogatz S H 1998 Nature 393 440
[30] Klemm K, Serrano M , Eguluz V M, San Miguel M 2012 Sci. Rep. 2 292
[31] Centola D 2010 Science 329 1194
[32] Bond R M, Fariss C J, Jones J J, Kramer A D, Marlow C, Settle J E, Fowler J H 2012 Nature 489 295
[33] Gao Z K, Yang Y X, Fang P C, Jin N D, Xia C Y, Hu L D 2015 Sci. Rep. 5 8222
[34] Gao Z K, Fang P C, Ding M S, Jin N D 2015 Experimental Thermal Fluid Science 60 157
[35] Holme P, Kim B J 2002 Phys. Rev. E 65 026107
[36] Pastor S R, Vzquez A, Vespignani A 2001 Phys. Rev. Lett. 87 258701
[37] Kendall M G 1938 Biometrika 30 81
[38] Papadopoulos F, Kitsak M, Serrano M , Bogu M, Krioukov D 2012 Nature 489 537
[39] Zhang Z Z, Xu W J, Zeng S Y 2014 Chin. Phys. B 23 088902
[40] Barabsi A L, Albert R 1999 Science 286 509
[41] Lu Y L, Jiang G P, Song Y R 2012 Chin. Phys. B 21 100207.
[42] Holme P, Saramki J 2012 Phys. Rep. 519 97
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