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The detecting of clusters or communities in large real-world networks such as large social or information networks is of considerable significance. We propose a new weighted evolving model of high clustering scale-free network incorporating a community structure mechanism, which means the addition of the new node depends on not only a single node but also a community. In the process of the evolution, a new node with probability p and a new community with the probability 1–p are added to the network. Different from the existing studies where new links are additionally established, some links with probability φ according to the triad formation mechanism and other links with the probability 1–φ according to the random selection mechanism are connected between neighbors in the model. The topology and weights of links of the network evolve as time goes on. Moreover, the evolving model gives power-law distributions of degree, weight, and strength as confirmed in several real world systems. Especially, the average clustering coefficient exhibits power-law decay as a function of degree of node. Both the community structure and the triad formation can enhance the average clustering coefficient of scale-free networks. Furthermore, we investigate how the synchronization of the network is influenced by the evolution mechanism of the network. Numerical simulation results show that the network synchronizability is optimized when the average clustering coefficient decreases in the model.
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Keywords:
- scale-free network /
- weighted network /
- clustering coefficient /
- synchronizability
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[2] Barabási A L, Albert R 1999 Science 286 509
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[5] Yao H X, Wang S G 2012 Chin. Phys. B 21 110506
[6] Liu Z R, Li Y, Zhang J B 2008 Chin. Phys. Lett. 25 874
[7] Fan J, Wang X F 2005 Physica A 349 443
[8] Wang X F, Chen G R 2002 Int. J. Bifurcat. Chaos 12 187
[9] Barahona M, Pecora L M 2002 Phys. Rev. Lett. 89 054101
[10] Wang X F, Chen G R 2002 IEEE Trans. Circuits Syst. I 49 54
[11] Yook S H, Jeong H, Barabási A L, Tu Y 2001 Phys. Rev. Lett. 86 5835
[12] Zheng D F, Trimper S, Zheng B, Hui P M 2003 Phys. Rev. E 67 040102
[13] Wang S J, Zhang C H 2004 Phys. Rev. E 70 066127
[14] Barrat A, Barthelemy M, Vespignani A 2004 Phys. Rev. Lett. 92 228701
[15] Ou Q, Jin Y D, Zhou T, Wang B H, Yin B Q 2007 Phys. Rev. E 75 021102
[16] Wang W X, Hu B, Zhou T, Wang B H, Xie Y B 2005 Phys. Rev. E 72 046140
[17] Xie Y B, Wang W X, Wang B H 2007 Phys. Rev. E 75 026111
[18] Wang W X, Hu B, Wang B H, Yan G 2006 Phys. Rev. E 73 016133
[19] Wang D, Jin X Z 2012 Acta Phys. Sin. 61 228901 (in Chinese) [王丹, 金小峥 2012 61 228901]
[20] Jing Y W, Hao B B, Zhang S Y 2009 Comp. Sysm. Comp. Sci. 6 87 (in Chinese) [井元伟, 郝彬彬, 张嗣瀛 2009 复杂系统与复杂性科学 6 87]
[21] Newman M E J 2003 SIAM Rev. 45 167
[22] Wang D, Jing Y W, Hao B B 2012 Acta Phys. Sin. 61 220511 (in Chinese) [王丹, 井元伟, 郝彬彬 2012 61 220511]
[23] Wang D, Jing Y W, Hao B B 2012 Acta Phys. Sin. 61 170513 (in Chinese) [王丹, 井元伟, 郝彬彬 2012 61 170513]
[24] Kocarev L, Amato P 2005 Chaos 15 024101
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[1] Watts D J, Strogatz S H 1998 Nature 393 440
[2] Barabási A L, Albert R 1999 Science 286 509
[3] Zhao M, Zhou T, Chen G R, Wang B H 2008 Prog. Phys. 28 22 (in Chinese) [赵明, 周涛, 陈关荣, 汪秉宏 2008 物理学进展 28 22]
[4] Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D U 2006 Phys. Rep. 424 175
[5] Yao H X, Wang S G 2012 Chin. Phys. B 21 110506
[6] Liu Z R, Li Y, Zhang J B 2008 Chin. Phys. Lett. 25 874
[7] Fan J, Wang X F 2005 Physica A 349 443
[8] Wang X F, Chen G R 2002 Int. J. Bifurcat. Chaos 12 187
[9] Barahona M, Pecora L M 2002 Phys. Rev. Lett. 89 054101
[10] Wang X F, Chen G R 2002 IEEE Trans. Circuits Syst. I 49 54
[11] Yook S H, Jeong H, Barabási A L, Tu Y 2001 Phys. Rev. Lett. 86 5835
[12] Zheng D F, Trimper S, Zheng B, Hui P M 2003 Phys. Rev. E 67 040102
[13] Wang S J, Zhang C H 2004 Phys. Rev. E 70 066127
[14] Barrat A, Barthelemy M, Vespignani A 2004 Phys. Rev. Lett. 92 228701
[15] Ou Q, Jin Y D, Zhou T, Wang B H, Yin B Q 2007 Phys. Rev. E 75 021102
[16] Wang W X, Hu B, Zhou T, Wang B H, Xie Y B 2005 Phys. Rev. E 72 046140
[17] Xie Y B, Wang W X, Wang B H 2007 Phys. Rev. E 75 026111
[18] Wang W X, Hu B, Wang B H, Yan G 2006 Phys. Rev. E 73 016133
[19] Wang D, Jin X Z 2012 Acta Phys. Sin. 61 228901 (in Chinese) [王丹, 金小峥 2012 61 228901]
[20] Jing Y W, Hao B B, Zhang S Y 2009 Comp. Sysm. Comp. Sci. 6 87 (in Chinese) [井元伟, 郝彬彬, 张嗣瀛 2009 复杂系统与复杂性科学 6 87]
[21] Newman M E J 2003 SIAM Rev. 45 167
[22] Wang D, Jing Y W, Hao B B 2012 Acta Phys. Sin. 61 220511 (in Chinese) [王丹, 井元伟, 郝彬彬 2012 61 220511]
[23] Wang D, Jing Y W, Hao B B 2012 Acta Phys. Sin. 61 170513 (in Chinese) [王丹, 井元伟, 郝彬彬 2012 61 170513]
[24] Kocarev L, Amato P 2005 Chaos 15 024101
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