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大量研究表明分形尺度特性广泛存在于真实复杂系统中, 且分形结构显著影响网络上的传播动力学行为. 虽然复杂网络的节点传播影响力吸引了越来越多学者的关注, 但依旧缺乏针对分形网络结构的节点影响力的系统研究. 鉴于此, 本文基于花簇分形网络模型, 研究了分形无标度结构上的节点传播影响力. 首先, 对比了不同分形维数下的节点影响力, 结果表明, 当分形维数很小时, 节点影响力的区分度几乎不随节点度变化, 很难区分不同节点的传播影响力, 而随着分形维数的增大, 从全局和局域角度都能很容易识别网络中的超级传播源. 其次, 通过对原分形网络进行不同程度的随机重连来分析网络噪声对节点影响力区分度的影响, 发现在低维分形网络上, 加入网络噪声之后能够容易区分不同节点的影响力, 而在无穷维超分形网络中, 加入网络噪声之后能够区分中间度节点的影响力, 但从全局和局域角度都很难识别中心节点的影响力. 所得结论进一步补充、深化了基于花簇分形网络的节点影响力研究, 研究结果对实际病毒传播的预警控制提供了一定的理论借鉴.Extensive studies have shown that the fractal scaling exists widely in real complex systems, and the fractal structure significantly affects the spreading dynamics on the networks. Although node influence in spreading dynamics of complex networks has attracted more and more attention, systematical studies about the node influence of fractal networks are still lacking. Based on the flower model, node influences of the fractal scale-free structures are studied in this paper. Firstly, the node influences of different fractal dimensions are compared. The results indicate that when the fractal dimension is very low, the discriminability of node influences almost does not vary with node degree, thus it is difficult to distinguish the influences of different nodes. With the increase of fractal dimension, it is easy to recognize the super-spreader from both the global and local viewpoints. In addition, the network noise is introduced by randomly rewiring the links of the original fractal networks, and the effect of network noise on the discriminability of node influence is analyzed. The results show that in fractal network with low dimension, it becomes easier to distinguish the influences of different nodes after adding network noises. In the fractal networks of infinite dimensions, the existence of network noises makes it possible to recognize the influences of medium nodes. However it is difficult to recognize the influences of central nodes from either the global or local perspective.
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Keywords:
- fractal structure /
- epidemic spreading /
- influence /
- discriminability
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[2] Song C, Havlin S, Makse H A 2006 Nat. Phys. 2 275
[3] Song C, Gallos L K, Havlin S, Makse H A 2007 J. Stat. Mech. P03006
[4] Kim J S, Goh K I, Kahng B, Kim D 2007 Chaos 17 026116
[5] Kitsak M, Havlin S, Paul G, Riccaboni M, Pammolli F, Stanley H E 2007 Phys. Rev. E 75 056115
[6] Zhang Z Z, Zhou S G, Zou T 2007 Eur. Phys. J. B 56 259
[7] Hinczewski M 2007 Phys. Rev. E 75 061104
[8] Zhang Z Z, Xie W L, Zhou S G, Gao S Y, Guan J H 2009 Europhys. Lett. 88 10001
[9] Zhang Z Z, Zhou S G, Zou T, Chen G S 2008 J. Stat. Mech. P09008
[10] Rozenfeld H D, Havlin S, ben-Avraham D 2007 New J. Phys. 9 175
[11] Lee H K, Shim P S, Noh J D 2013 Phys. Rev. E 87 062812
[12] 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]
[13] Gong K, Tang M, Hui P M, Zhang H F, Do Y, Lai Y C 2013 PLos ONE 8 e83489
[14] Li R Q, Tang M, Hui B M 2013 Acta Phys. Sin. 62 168903 (in Chinese) [李睿琪, 唐明, 许伯铭 2013 62 168903]
[15] Pastor-Satorras R, Vespignani A 2002 Phys. Rev. E 65 036104
[16] Kitsak M, Gallos L K, Havlin S, Liljeros F, Muchnik L, Stanley H E, Makse H A 2010 Nat. Phys. 6 888
[17] Chung N N, Chew L Y, Zhou J, Lai C H 2012 Europhys. Lett. 98 58004
[18] Chen D B, L L Y, Shang M S, Zhang Y C, Zhou T 2012 Physica A 391 1777
[19] Bauer F, Lizier J T 2012 Europhys. Lett. 99 68007
[20] Costa L da F, Rodrigues F A, Travieso G, Boas P R V 2007 Adv. Phys. 56 167
[21] Pu J, Chen X W, Wei D J, Liu Q, Deng Y 2014 Europhys. Lett. 107 10010
[22] Anderson R M, May R M 1992 Infectious Disease of Humans (Oxford: Oxford University Press) pp1-768
[23] Castellano C, Pastor-Satorras R 2006 Phys. Rev. Lett. 96 038701
[24] Shu P P, Tang M, Gong K, Liu Y 2012 Chaos 22 043124
[25] Barthélemy M, Barrat A, Pastor-Satorras R, Vespignani A 2004 Phys. Rev. Lett. 92 178701
[26] Yang H, Tang M, Zhang H F 2012 New J. Phys. 14 123017
[27] Wang W, Tang M, Zhang H F, Gao H, Do Y, Liu Z H 2014 Phys. Rev. E 90 042803
[28] L L Y, Zhang Y C, Yeung C H, Zhou T 2011 PLoS ONE 6 e21202
[29] Guimerá R, Sales-Pardo M 2009 Proc. Natl. Acad. Sci. USA 106 22073
[30] Legrain P, Wojcik J, Gauthier J M 2001 Trends in Genetics 17 346
[31] Marsden P V 1990 Annual Review of Sociology 16 435
[32] Newman M E J 2002 Phys. Rev. Lett. 89 208701
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[1] Song C, Havlin S, Makse H A 2005 Nature 433 392
[2] Song C, Havlin S, Makse H A 2006 Nat. Phys. 2 275
[3] Song C, Gallos L K, Havlin S, Makse H A 2007 J. Stat. Mech. P03006
[4] Kim J S, Goh K I, Kahng B, Kim D 2007 Chaos 17 026116
[5] Kitsak M, Havlin S, Paul G, Riccaboni M, Pammolli F, Stanley H E 2007 Phys. Rev. E 75 056115
[6] Zhang Z Z, Zhou S G, Zou T 2007 Eur. Phys. J. B 56 259
[7] Hinczewski M 2007 Phys. Rev. E 75 061104
[8] Zhang Z Z, Xie W L, Zhou S G, Gao S Y, Guan J H 2009 Europhys. Lett. 88 10001
[9] Zhang Z Z, Zhou S G, Zou T, Chen G S 2008 J. Stat. Mech. P09008
[10] Rozenfeld H D, Havlin S, ben-Avraham D 2007 New J. Phys. 9 175
[11] Lee H K, Shim P S, Noh J D 2013 Phys. Rev. E 87 062812
[12] 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]
[13] Gong K, Tang M, Hui P M, Zhang H F, Do Y, Lai Y C 2013 PLos ONE 8 e83489
[14] Li R Q, Tang M, Hui B M 2013 Acta Phys. Sin. 62 168903 (in Chinese) [李睿琪, 唐明, 许伯铭 2013 62 168903]
[15] Pastor-Satorras R, Vespignani A 2002 Phys. Rev. E 65 036104
[16] Kitsak M, Gallos L K, Havlin S, Liljeros F, Muchnik L, Stanley H E, Makse H A 2010 Nat. Phys. 6 888
[17] Chung N N, Chew L Y, Zhou J, Lai C H 2012 Europhys. Lett. 98 58004
[18] Chen D B, L L Y, Shang M S, Zhang Y C, Zhou T 2012 Physica A 391 1777
[19] Bauer F, Lizier J T 2012 Europhys. Lett. 99 68007
[20] Costa L da F, Rodrigues F A, Travieso G, Boas P R V 2007 Adv. Phys. 56 167
[21] Pu J, Chen X W, Wei D J, Liu Q, Deng Y 2014 Europhys. Lett. 107 10010
[22] Anderson R M, May R M 1992 Infectious Disease of Humans (Oxford: Oxford University Press) pp1-768
[23] Castellano C, Pastor-Satorras R 2006 Phys. Rev. Lett. 96 038701
[24] Shu P P, Tang M, Gong K, Liu Y 2012 Chaos 22 043124
[25] Barthélemy M, Barrat A, Pastor-Satorras R, Vespignani A 2004 Phys. Rev. Lett. 92 178701
[26] Yang H, Tang M, Zhang H F 2012 New J. Phys. 14 123017
[27] Wang W, Tang M, Zhang H F, Gao H, Do Y, Liu Z H 2014 Phys. Rev. E 90 042803
[28] L L Y, Zhang Y C, Yeung C H, Zhou T 2011 PLoS ONE 6 e21202
[29] Guimerá R, Sales-Pardo M 2009 Proc. Natl. Acad. Sci. USA 106 22073
[30] Legrain P, Wojcik J, Gauthier J M 2001 Trends in Genetics 17 346
[31] Marsden P V 1990 Annual Review of Sociology 16 435
[32] Newman M E J 2002 Phys. Rev. Lett. 89 208701
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