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The relations between two highly clustered scale-free network evolution mechanisms and synchronizability are studied in this paper. Firstly, we propose an extended Holme and Kim (EHK) model with adjustive clustering coefficients and power-law exponent based on the Holme and Kim (HK) model. Triad formation mechanism is extended among old nodes compared with the HK model. And the following shortages of HK modle are settled: there is no link evolution in old nodes and the numbers of links of a new node adding to network is fixed. Secondly, the effect of triad formation on synchronizability in an unweighted network is investigated. Finally, simulation results show that the triad formation mechanism can weaken the synchronizability of both types of networks.
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Keywords:
- scale-free network /
- clustering coefficient /
- synchronizability
[1] Lü L, Li G, Cai Y 2008 Acta Phys. Sin. 57 7517(in Chinese) [吕翎, 李钢, 柴元2008 57 7517]
[2] Yang X K, Cai L, Zhao X H, Feng Z W 2008 Acta Phys. Sin. 59 3740 (in Chinese) [杨晓阔, 蔡理, 赵晓辉, 冯朝文2010 59 3740]
[3] Li J, Wang B H, Jiang P Q, Zhou T, Wang W X 2006 Acta Phys. Sin. 55 4051 (in Chinese) [李季, 汪秉宏, 蒋品群, 周涛, 王文旭2006 55 4051]
[4] Watts D J, Strogatz S H 1998 Nature (London) 393 440
[5] Barabási A L, Albert R 1999 Science 286 509
[6] Gao J X, Havlin S, Xu X M, Stanley E H 2011 Phys. Rev. E 84 046115
[7] Yuan W J, Zhou C S 2011 Phys. Rev. E 84 016116
[8] Zeng A, Son S W, Yeung C H, Fan Y, Di Z 2011 Phys. Rev. E 83 045101
[9] Watanabe T, Masuda N 2010 Phys. Rev. E 82 046102
[10] Gorochowski T E, Bernardo M D, Grierson C S 2010 Phys. Rev. E 81 056212
[11] Zhu J F, Zhao M, Yu W W, Zhou C S, Wang B H 2010 Phys. Rev. E 81 026201
[12] Holme P, Kim B J 2002 Phys. Rev. E 65 026107
[13] Li W G, Wang L H, Chen M F 2009 Comp. Eng. 35 121 (in Chinese) [李稳国, 王力虎, 陈明芳 2009计算机工程 35 121]
[14] Zhang Z Z, Rong L L, Wang B, Zhou S G, Guan J H 2007 Physica A 380 639
[15] Pan X F, Wang X F 2006 Acta Phys. Sin. 55 4058 (in Chinese) [潘灶烽, 汪小帆2006 55 4058]
[16] Wu X, Wang B H, Zhou T, Wang W X, Zhao M, Yang H J 2006 Chin. Phys. Lett. 23 1046
[17] Zhou T, Xiao W K, Ren J, Wang B H 2007 Complex Syst. Complex Sci. 4 10 (in Chinese) [周涛, 肖伟科, 任捷, 汪秉宏 2007复杂系统与复杂性科学 4 10]
[18] Xiao W K, Ren J, Feng Q, Song Z W, Zhu M X, Yang H F, Jin H Y, Wang B H, Zhou T 2007 Phys. Rev. E 76 037102
[19] Yang H X, Wang B H, Liu J G, Han X P, Zhou T 2008 Chin. Phys. Lett. 25 2718
[20] Cui A X, Fu Y, Shang M S, Chen R B, Zhou T 2011 Acta Phys.Sin. 60 038901 (in Chinese) [崔爱香, 傅彦, 尚明生, 陈端兵, 周涛2011 60 038901]
[21] Barrat A, Barthelemy M, Vespignani A 2004 Phys. Rev. Lett. 92 228701
[22] Wang B, Zhou T, Xiu Z L, Kim B J 2007 Eur. Phys. J. B 60 89
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[1] Lü L, Li G, Cai Y 2008 Acta Phys. Sin. 57 7517(in Chinese) [吕翎, 李钢, 柴元2008 57 7517]
[2] Yang X K, Cai L, Zhao X H, Feng Z W 2008 Acta Phys. Sin. 59 3740 (in Chinese) [杨晓阔, 蔡理, 赵晓辉, 冯朝文2010 59 3740]
[3] Li J, Wang B H, Jiang P Q, Zhou T, Wang W X 2006 Acta Phys. Sin. 55 4051 (in Chinese) [李季, 汪秉宏, 蒋品群, 周涛, 王文旭2006 55 4051]
[4] Watts D J, Strogatz S H 1998 Nature (London) 393 440
[5] Barabási A L, Albert R 1999 Science 286 509
[6] Gao J X, Havlin S, Xu X M, Stanley E H 2011 Phys. Rev. E 84 046115
[7] Yuan W J, Zhou C S 2011 Phys. Rev. E 84 016116
[8] Zeng A, Son S W, Yeung C H, Fan Y, Di Z 2011 Phys. Rev. E 83 045101
[9] Watanabe T, Masuda N 2010 Phys. Rev. E 82 046102
[10] Gorochowski T E, Bernardo M D, Grierson C S 2010 Phys. Rev. E 81 056212
[11] Zhu J F, Zhao M, Yu W W, Zhou C S, Wang B H 2010 Phys. Rev. E 81 026201
[12] Holme P, Kim B J 2002 Phys. Rev. E 65 026107
[13] Li W G, Wang L H, Chen M F 2009 Comp. Eng. 35 121 (in Chinese) [李稳国, 王力虎, 陈明芳 2009计算机工程 35 121]
[14] Zhang Z Z, Rong L L, Wang B, Zhou S G, Guan J H 2007 Physica A 380 639
[15] Pan X F, Wang X F 2006 Acta Phys. Sin. 55 4058 (in Chinese) [潘灶烽, 汪小帆2006 55 4058]
[16] Wu X, Wang B H, Zhou T, Wang W X, Zhao M, Yang H J 2006 Chin. Phys. Lett. 23 1046
[17] Zhou T, Xiao W K, Ren J, Wang B H 2007 Complex Syst. Complex Sci. 4 10 (in Chinese) [周涛, 肖伟科, 任捷, 汪秉宏 2007复杂系统与复杂性科学 4 10]
[18] Xiao W K, Ren J, Feng Q, Song Z W, Zhu M X, Yang H F, Jin H Y, Wang B H, Zhou T 2007 Phys. Rev. E 76 037102
[19] Yang H X, Wang B H, Liu J G, Han X P, Zhou T 2008 Chin. Phys. Lett. 25 2718
[20] Cui A X, Fu Y, Shang M S, Chen R B, Zhou T 2011 Acta Phys.Sin. 60 038901 (in Chinese) [崔爱香, 傅彦, 尚明生, 陈端兵, 周涛2011 60 038901]
[21] Barrat A, Barthelemy M, Vespignani A 2004 Phys. Rev. Lett. 92 228701
[22] Wang B, Zhou T, Xiu Z L, Kim B J 2007 Eur. Phys. J. B 60 89
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