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Random walk has been applied to exploring the effective transport strategy of data package in complex networks. Because the disassortative degree correlation is ubiquitous in technical networks including the internet, we study the biased random walks in the scale-free networks with the disassortative degree correlation. Computer simulation shows that the degree correlation changes the behavior of the random walk. Random walkers are located on small degree nodes with a low probability, and they can be distributed homogeneously on other nodes. We find out the optimal biased coefficient that ensures the most homogeneous distribution on large nodes. In the optimal case, the degree-correlated network exhibits a more efficient random walk than degree-uncorrelated networks. We propose the mechanism for the effect of the disassortative mixing on the random walk.
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Keywords:
- complex network /
- scale-free network /
- random walk /
- degree correlation
[1] Wang K, Zhou S Y, Zhang Y F, Pei W J, Liu Q 2011 Acta Phys. Sin. 60 118903 (in Chinese) [王开, 周思源, 张毅峰, 裴文江, 刘茜 2011 物理学报 60 118903]
[2] Jia X, Hong J S, Yang H C, Yang C, Shi X H, Hu J Q 2014 Chin. Phys. B 23 076401
[3] Barabási A L, Albert R 1999 Science 286 509
[4] Wang D L, Yu Z G, Anh V 2012 Chin. Phys. B 21 080504
[5] Fronczak A, Fronczak P 2009 Phys. Rev. E 80 016107
[6] Vazquez A, Moreno Y 2003 Phys. Rev. E 67 015101c
[7] Pastor-Satorras R, Vazquezand A, Vespignani A 2001 Phys. Rev. Lett. 87 258701
[8] Tadic B, Thurnerb S 2004 Physica A 332 566
[9] Wu W, Jiang F M, Zeng J B 2014 Acta Phys. Sin. 63 048202 (in Chinese) [吴伟, 蒋方明, 曾建邦 2014 物理学报 63 048202]
[10] Song L J, Tang G, Zhang Y W, Han K, Xu Z P, Xia H, Hao D P, Li Y 2014 Chin. Phys. B 23 010503
[11] Wang Y Q, Yang X Y 2013 Chin. Phys. B 22 010509
[12] Liu J, Bao J D 2013 Chin. Phys. Lett. 30 020202
[13] Jiang Z Y, Wang H, Gao C 2011 Acta Phys. Sin. 60 058903 (in Chinese) [姜志远, 王晖, 高超 2011 物理学报 60 058903]
[14] Li S B, Lou L L, Chen R X, Hong L 2014 Acta Phys. Sin. 63 028901 (in Chinese) [李世宝, 娄琳琳, 陈瑞祥, 洪利 2014 物理学报 63 028901]
[15] Liu G, Li Y S 2012 Acta Phys. Sin. 61 248901 (in Chinese) [刘刚, 李永树 2012 物理学报 61 248901]
[16] Noh J D, Rieger H 2004 Phys. Rev. Lett. 92 118701
[17] Wang S J, Wu A C, Wu Z X, Xu X J, Wang Y H 2007 Phys. Rev. E 75 046113
[18] Newman M E J 2002 Phys. Rev. Lett. 89 208701
[19] Chen Q H, Shi D H 2003 Physica A 335 240
[20] Wang W X, Wang B H, Yin C Y, Xie Y B, Zhou T 2006 Phys. Rev. E 73 026111
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[1] Wang K, Zhou S Y, Zhang Y F, Pei W J, Liu Q 2011 Acta Phys. Sin. 60 118903 (in Chinese) [王开, 周思源, 张毅峰, 裴文江, 刘茜 2011 物理学报 60 118903]
[2] Jia X, Hong J S, Yang H C, Yang C, Shi X H, Hu J Q 2014 Chin. Phys. B 23 076401
[3] Barabási A L, Albert R 1999 Science 286 509
[4] Wang D L, Yu Z G, Anh V 2012 Chin. Phys. B 21 080504
[5] Fronczak A, Fronczak P 2009 Phys. Rev. E 80 016107
[6] Vazquez A, Moreno Y 2003 Phys. Rev. E 67 015101c
[7] Pastor-Satorras R, Vazquezand A, Vespignani A 2001 Phys. Rev. Lett. 87 258701
[8] Tadic B, Thurnerb S 2004 Physica A 332 566
[9] Wu W, Jiang F M, Zeng J B 2014 Acta Phys. Sin. 63 048202 (in Chinese) [吴伟, 蒋方明, 曾建邦 2014 物理学报 63 048202]
[10] Song L J, Tang G, Zhang Y W, Han K, Xu Z P, Xia H, Hao D P, Li Y 2014 Chin. Phys. B 23 010503
[11] Wang Y Q, Yang X Y 2013 Chin. Phys. B 22 010509
[12] Liu J, Bao J D 2013 Chin. Phys. Lett. 30 020202
[13] Jiang Z Y, Wang H, Gao C 2011 Acta Phys. Sin. 60 058903 (in Chinese) [姜志远, 王晖, 高超 2011 物理学报 60 058903]
[14] Li S B, Lou L L, Chen R X, Hong L 2014 Acta Phys. Sin. 63 028901 (in Chinese) [李世宝, 娄琳琳, 陈瑞祥, 洪利 2014 物理学报 63 028901]
[15] Liu G, Li Y S 2012 Acta Phys. Sin. 61 248901 (in Chinese) [刘刚, 李永树 2012 物理学报 61 248901]
[16] Noh J D, Rieger H 2004 Phys. Rev. Lett. 92 118701
[17] Wang S J, Wu A C, Wu Z X, Xu X J, Wang Y H 2007 Phys. Rev. E 75 046113
[18] Newman M E J 2002 Phys. Rev. Lett. 89 208701
[19] Chen Q H, Shi D H 2003 Physica A 335 240
[20] Wang W X, Wang B H, Yin C Y, Xie Y B, Zhou T 2006 Phys. Rev. E 73 026111
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