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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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[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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[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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