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针对现实世界的网络中普遍存在的层级结构建立一个级联失效模型, 该模型可用于优化金融、物流网络设计. 选择的层级网络模型具有树形骨架和异质的隐含连接, 并且骨架中每层节点拥有的分枝数服从正态分布. 级联失效模型中对底层节点的打击在不完全信息条件下进行, 也即假设打击者无法观察到隐含连接. 失效节点的负载重分配考虑了层级异质性, 它可以选择倾向于向同级或高层级完好节点分配额外负载. 仿真实验表明, 层级网络的拓扑结构随连接参数变化逐渐从小世界网络过渡到随机网络. 网络级联失效规模随隐含连接比例呈现出先增加后降低的规律. 负载重分配越倾向于高层级节点, 网络的抗毁损性越高. 同时, 由于连接参数会改变隐含连接在不同层级之间的分布, 进而对网络的抗毁损性产生显著影响, 为了提高网络抗毁损能力, 设计网络、制定管理控制策略时应合理设定连接参数.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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