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In this paper, we proposes a cascading failure model for the complex network with hierarchy structure which is common in real networks. This model can be used to optimize the financial or logistic network design. The hierarchy network has a tree-shape backbone and many random hidden linkages. The branches of each node in the backbone follow normal distribution. The attack on the network is from bottom layer under the condition of incomplete information, i.e., on the assumption that the attacker cannot observe the hidden linkages. The load redistribution of the failure nodes takes into consideration the hierarchy heterogeneity, of which the network tends to redistribute extra load to intact nodes of the same or higher hierarchies. Simulation experiment shows that the topology of hierarchy network changes from small world network into random network with the variation of linkage parameters. The size of cascading failure firstly increases and then decreases with the hidden linkage ratio increasing and the network shows higher robustness when the load of failure node is redistributed to the intact node with high hierarchy. The experiments also demonstrate that the linkage parameters play a significant role in the robustness of the network because these parameters can affect the hierarchy distribution of hidden links. Therefore, in order to achieve better robustness of network, we should reasonably choose parameters in topology design and network control strategies.
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Keywords:
- complex network /
- cascading failure /
- hierarchy structure
[1] Watts D J, Strogatz S H 1998 Nature 393 440
[2] Barabási A L, Albert R 1999 Science 286 509
[3] Tabak B M, Takami M, Rocha J M 2014 Physica A 394 211
[4] Heiberger R H 2014 Physica A 393 376
[5] Zhang Y C, Liu Y, Zhang H F, Cheng H, Xiong F 2011 Acta Phys. Sin. 60 050501 (in Chinese) [(张彦超, 刘云, 张海峰, 程辉, 熊菲 2011 物理学报 60 050501]
[6] Jalili M 2013 Physica A 392 959
[7] Lei T, Yu Z W 2007 Com. Eng. Appl. 43 132 (in Chinese) [雷霆, 余镇危 2007 43 132]
[8] Zheng X, Chen J P, Shao J L, Bie L D 2012 Acta Phys. Sin. 61 190510 (in Chinese) [郑啸, 陈建平, 邵佳丽, 别立东 2012 物理学报 61 190510]
[9] Ling X, Hu M S, Long J C, Ding J X, Shi Q 2013 Chin. Phys. B 22 018904
[10] Albert R, Jeong H, Barabási A L 2000 Nature 406 378
[11] Motter A E, Lai Y C 2002 Phys. Rev. E 66 065102
[12] Bao Z J, Cao Y J, Ding L J 2009 Physica A 388 4491
[13] Moreira A A, Andrade J S, Herrmann H J, Indekeu J O 2009 Phys. Rev. Lett. 102 018701
[14] Chen S M, Pang S P, Zou X Q 2013 Chin. Phys. B 22 058901
[15] Mirzasoleiman B, Babaei M, Jalili M, Safari M 2011 Phys. Rev. E 84 046114
[16] Zheng J F, Gao Z Y, Fu B B, Li F 2009 Chin. Phys. B 4754
[17] McNerney J, Fath B D, Silverberg G 2013 Physica A 392 6427
[18] Mantegna R N 1999 Eur. J. Phys. B 11 193
[19] Dodds P S, Watts D J, Sabel C F 2003 PNAS 100 12516
[20] Li P, Wang B H, Sun H, Gao P, Zhou T 2008 Eur. J. Phys. B 62 101
[21] He D R, Liu Z H, Wang B H 2008 Complex System and Complex Network (in Chinese) [何大韧, 刘宗华, 汪秉宏 2008 复杂系统与复杂网络 (北京: 高等教育出版社)]
[22] Duan D L, Wu X Y 2014 Acta Phys. Sin. 63 030501 (in Chinese) [段东立, 武小悦 2014 物理学报 63 030501]
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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] Tabak B M, Takami M, Rocha J M 2014 Physica A 394 211
[4] Heiberger R H 2014 Physica A 393 376
[5] Zhang Y C, Liu Y, Zhang H F, Cheng H, Xiong F 2011 Acta Phys. Sin. 60 050501 (in Chinese) [(张彦超, 刘云, 张海峰, 程辉, 熊菲 2011 物理学报 60 050501]
[6] Jalili M 2013 Physica A 392 959
[7] Lei T, Yu Z W 2007 Com. Eng. Appl. 43 132 (in Chinese) [雷霆, 余镇危 2007 43 132]
[8] Zheng X, Chen J P, Shao J L, Bie L D 2012 Acta Phys. Sin. 61 190510 (in Chinese) [郑啸, 陈建平, 邵佳丽, 别立东 2012 物理学报 61 190510]
[9] Ling X, Hu M S, Long J C, Ding J X, Shi Q 2013 Chin. Phys. B 22 018904
[10] Albert R, Jeong H, Barabási A L 2000 Nature 406 378
[11] Motter A E, Lai Y C 2002 Phys. Rev. E 66 065102
[12] Bao Z J, Cao Y J, Ding L J 2009 Physica A 388 4491
[13] Moreira A A, Andrade J S, Herrmann H J, Indekeu J O 2009 Phys. Rev. Lett. 102 018701
[14] Chen S M, Pang S P, Zou X Q 2013 Chin. Phys. B 22 058901
[15] Mirzasoleiman B, Babaei M, Jalili M, Safari M 2011 Phys. Rev. E 84 046114
[16] Zheng J F, Gao Z Y, Fu B B, Li F 2009 Chin. Phys. B 4754
[17] McNerney J, Fath B D, Silverberg G 2013 Physica A 392 6427
[18] Mantegna R N 1999 Eur. J. Phys. B 11 193
[19] Dodds P S, Watts D J, Sabel C F 2003 PNAS 100 12516
[20] Li P, Wang B H, Sun H, Gao P, Zhou T 2008 Eur. J. Phys. B 62 101
[21] He D R, Liu Z H, Wang B H 2008 Complex System and Complex Network (in Chinese) [何大韧, 刘宗华, 汪秉宏 2008 复杂系统与复杂网络 (北京: 高等教育出版社)]
[22] Duan D L, Wu X Y 2014 Acta Phys. Sin. 63 030501 (in Chinese) [段东立, 武小悦 2014 物理学报 63 030501]
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