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Motivated by the observations that the weight of a link in realistic networks is strongly correlated with the product of the corresponding degrees, we present an asymmetrical weighted scheme relating to the degrees of starting point and terminal point, and investigate the effects of weighted scheme on synchronizability in light of different network structures. The results show that the more heterogeneous the degree distribution of network, the more remarkable the effect on enhanced synchronizability by the weighted method is. However, there is little effect on enhanced synchronizability by the weighted method for the homogeneous random network. It is shown that no matter whether small world networks or scale-free networks, the synchronizability is maximal when the total strength of all in-links of every node is equal to one.
[1] Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D U 2006 Phys. Rep. 424 175
[2] Zhao M, Wang B B, Jiang P Q, Zhou T 2005 Prog. in Phys. 25 273 (in Chinese) [赵明, 汪秉宏, 蒋品群, 周涛 2005 物理学进展 25 273]
[3] Zhao M, Zhou T, Chen G R, Wang B B 2008 Prog. in Phys. 28 22 (in Chinese) [赵明, 周涛, 陈关荣, 汪秉宏 2008 物理学进展 28 22]
[4] Metz F L, Neri I, Bollé D 2011 Phys. Rev. E 84 055101
[5] Lü L, Li G, Cai Y 2008 Acta Phys.Sin. 57 7517(in Chinese) [吕翎, 李钢, 柴元 2008 物理学报 57 7517]
[6] Yang X K, Cai L, Zhao X H, Feng Z W 2010 Acta Phys.Sin. 59 3740 (in Chinese) [杨晓阔, 蔡理, 赵晓辉, 冯朝文 2010 物理学报 59 3740]
[7] Cai M, Du H F, Ren Y K, Marcus W F 2011 Acta Phys.Sin. 60 110513 (in Chinese) [蔡萌, 杜海峰, 任义科, 费尔德曼 2011 物理学报 60 110513]
[8] Gao J X, Havlin S, Xu X M, Eugene Stanley H 2011 Phys. Rev. E 84 046115
[9] Yuan W J, Zhou C S 2011 Phys. Rev. E 84 016116
[10] Zeng A, Son S W, Yeung C H, Fan Y, Di Z 2011 Phys. Rev. E 83 045101
[11] Chavez M, Hwang D U, Amann A 2005 Phys. Rev. Lett. 94 218701
[12] Zhao M, Zhou T, Wang B H 2006 Eur. Phys. J. B 53 375
[13] Watanabe T, Masuda N 2010 Phys. Rev. E 82 046102
[14] Gorochowski T E, Bernardo M D, Grierson C S 2010 Phys. Rev. E 81 056212
[15] Zhu J F, Zhao M, Yu W W, Zhou C S, Wang B H 2010 Phys. Rev. E 81 026201
[16] Motter A E, Zhou C, Kurths J 2005 Phys. Rev. E 71 016116
[17] Motter A E, Zhou C, Kurths 2006 American Institute of Physics Conference Series 776 201
[18] Lu Y F, Zhao M, Zhou T, Wang B H 2007 Phys. Rev. E 76 057103
[19] Hwang D U, Chavez M, Amann A 2005 Phys. Rev. Lett. 94 138701
[20] Zou Y L, Zhu J, Chen G R 2006 Phys. Rev. E 74 046107
[21] Newman M E J, Watts D J 1999 Phys. Lett. A 263 341
[22] Barabási A L, Albert R 1999 Science 286 509
[23] Jesús G G, Moreno Y 2006 Phys. Rev. E 73 056124
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[1] Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D U 2006 Phys. Rep. 424 175
[2] Zhao M, Wang B B, Jiang P Q, Zhou T 2005 Prog. in Phys. 25 273 (in Chinese) [赵明, 汪秉宏, 蒋品群, 周涛 2005 物理学进展 25 273]
[3] Zhao M, Zhou T, Chen G R, Wang B B 2008 Prog. in Phys. 28 22 (in Chinese) [赵明, 周涛, 陈关荣, 汪秉宏 2008 物理学进展 28 22]
[4] Metz F L, Neri I, Bollé D 2011 Phys. Rev. E 84 055101
[5] Lü L, Li G, Cai Y 2008 Acta Phys.Sin. 57 7517(in Chinese) [吕翎, 李钢, 柴元 2008 物理学报 57 7517]
[6] Yang X K, Cai L, Zhao X H, Feng Z W 2010 Acta Phys.Sin. 59 3740 (in Chinese) [杨晓阔, 蔡理, 赵晓辉, 冯朝文 2010 物理学报 59 3740]
[7] Cai M, Du H F, Ren Y K, Marcus W F 2011 Acta Phys.Sin. 60 110513 (in Chinese) [蔡萌, 杜海峰, 任义科, 费尔德曼 2011 物理学报 60 110513]
[8] Gao J X, Havlin S, Xu X M, Eugene Stanley H 2011 Phys. Rev. E 84 046115
[9] Yuan W J, Zhou C S 2011 Phys. Rev. E 84 016116
[10] Zeng A, Son S W, Yeung C H, Fan Y, Di Z 2011 Phys. Rev. E 83 045101
[11] Chavez M, Hwang D U, Amann A 2005 Phys. Rev. Lett. 94 218701
[12] Zhao M, Zhou T, Wang B H 2006 Eur. Phys. J. B 53 375
[13] Watanabe T, Masuda N 2010 Phys. Rev. E 82 046102
[14] Gorochowski T E, Bernardo M D, Grierson C S 2010 Phys. Rev. E 81 056212
[15] Zhu J F, Zhao M, Yu W W, Zhou C S, Wang B H 2010 Phys. Rev. E 81 026201
[16] Motter A E, Zhou C, Kurths J 2005 Phys. Rev. E 71 016116
[17] Motter A E, Zhou C, Kurths 2006 American Institute of Physics Conference Series 776 201
[18] Lu Y F, Zhao M, Zhou T, Wang B H 2007 Phys. Rev. E 76 057103
[19] Hwang D U, Chavez M, Amann A 2005 Phys. Rev. Lett. 94 138701
[20] Zou Y L, Zhu J, Chen G R 2006 Phys. Rev. E 74 046107
[21] Newman M E J, Watts D J 1999 Phys. Lett. A 263 341
[22] Barabási A L, Albert R 1999 Science 286 509
[23] Jesús G G, Moreno Y 2006 Phys. Rev. E 73 056124
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