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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
[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 物理学报 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 物理学报 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 物理学报 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 物理学报 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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