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In this paper, we analyze the diffusion patterns of cascading failure, which happen in the express hypernetwork and electronic hypernetwork respectively. The cascading failure of the express hypernetwork is diffused by the node, and the cascading failure of the electronic hypernetwork is diffused by the hyper-edge. According to hyper-graph theory, we propose two methods to characterize these cascading failures, which are 2-section graph analytical method and line-graph analytical method. We analyze the characteristics of the cascading failures based on node by using the 2-section graph analytical method and based on hyper-edge by using line-graph analytical method, respectively. We construct a k uniform scale-free hypernetwork and analyze the cascading failure process of this hypernetwork based on the couple map lattice according to our methods. The simulation results show that the scale-free hypernetworks are both robust and vulnerable for attack. It is found that the cascading failure based on the node of k uniform scale-free hypernetwork is associated with the hyper-degree distribution of nodes, and the scale-free hypernetwork is robust for random attack and vulnerable for deliberate attack. The more nodes a hyper-edge has, the better robustness the hypernetwork has.The cascading failure based on the hyper-edge is different from the cascading failure based on the node. The cascading failure based on the hyper-edge is associated with the hyper-edge degree distribution. The hyper-edge degree distribution of the scale-free hypernetwork is not entirely the power-low distribution. When the cascading failure is diffused by the hyper-edge, the hypernetwork is vulnerable for random attack and robustness for deliberate attack if there are 3 or 5 nodes in a hyper-edge. Moreover, the hypernetwork becomes robust for the random attack if there are 7 nodes in a hyper-edge. Furthermore, the k uniform scale-free hypernetwork is more robust than the same size Barabasi-Albert scale-free network for the same attack. The cascading failure process based on the hyper-edge is slower than based on the node. We find that the edge number is another influential factor of robustness. The network is more robust if it has more edges for fixed node number. The line-graph has more edges than the 2-section graph in the same size scale-free hypernetwork, so the cascading failure of node is slower than that of hyper-edge.
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Keywords:
- hypergraph /
- scale-free hypernetwork /
- cascading failure /
- couple map lattice
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[14] Wang J P, G Q, Yang G Y, Liu J G 2015 Physica A 428 250
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[17] Buldyrev S V, Parshani R, Paul G, Stanley H E, Havlin S 2010 Nature 464 1025
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[19] Dong G G, Tian L X, Zhou D, Du R J, Xiao J, Stanley H E 2013 Euro. Lett. 102 68004
[20] Dong G G, Tian L X, Du R J, Stanley H E 2014 Physica A 394 370
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[22] Akram M, Dudek W A 2013 Inform. Sci. 218 182
[23] Rangasamy P, Akram M, Thilagavathi S 2013 Inform. Process. Lett. 113 599
[24] Segovia-Juarez J L, Colombano S 2003 BioSystems 68 187
[25] Berge C, Minieka E 1973 Graph and Hypergraph (North Holland: North-Holland Publishing Company Amsterdam) pp389-413
[26] Berge C, Sterboul F 1977 J. Comb. Theory B 22 97
[27] Estrada E, Rodrguez-Velzquez J A 2006 Physica A 364 581
[28] Volpentesta, A P 2008 Eur. J. Oper. Res. 188 390
[29] Pretolani D 2013 Eur. J. Oper. Res. 230 226
[30] Ghosal G, Zlatić V, Caldarelli G, Newman M E J 2009 Phys. Rev. E 79 066118
[31] Zlatić V, Ghoshal G, Caldarelli G 2009 Phys. Rev. E 80 036118
[32] Neubauer N, Obermayer K 2009 HT 09 Torino, Italy, June 29-July 1, 2009
[33] Bretto A 2013 Hypergraph Theory: An Introduction (New York: Springer Science Business Media)
[34] Peng X Z, Yao H, Du J, Wang Z, Ding C 2015 Acta Phys. Sin. 64 048901 (in Chinese) [彭兴钊, 姚宏, 杜军, 王哲, 丁超 2015 物理学报 64 048901]
[35] Chen S M, L H, Xu Q G, Xu Y F, Lai Q 2015 Acta Phys. Sin. 64 048902 (in Chinese) [陈世明, 吕辉, 徐青刚, 许云飞, 赖强 2015 物理学报 64 048902]
[36] Ding L, Zhang S Y 2012 Comput. Sci. 39 8 (in Chinese) [丁琳, 张嗣瀛 2012 计算机科学 39 8]
[37] Kanoko K 1992 Couple Map Lattice (Singapore: World Scientific)
[38] Wang X F, Xu J 2004 Phys. Rev. E 70 056113
[39] Xu J, Wang X F 2005 Physica A 349 685
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[1] Wang J J, Rong L L, Deng Q H, Zhang J Y 2010 Eur. Phys. J. B 77 493
[2] Zhang Z K, Liu C 2010 J. Stat. Mech. -Theory E 2010 10005
[3] Krawiecki A 2013 Acta Phys. Polon. A 123
[4] Gmez-Gardees J, Reinares I, Arenas A, Flora L M 2012 Sci. Reports 2 620
[5] Hu F, Zhao H X, Ma X J 2013 Sci. Sin.: Phys. Mech. Astron. 43 16 (in Chinese) [胡枫, 赵海兴, 马秀娟 2013 中国科学: 物理学 力学 天文学 43 16]
[6] Hu F, Zhao H X, He J B, Li F X, Li S L, Zhang Z K 2013 Acta Phys. Sin. 62 198901 (in Chinese) [胡枫, 赵海兴, 何佳培, 李发旭, 李淑玲, 张子柯 2013 物理学报 62 198901]
[7] Yang G Y, Liu J G 2014 Chin. Phys. B 23 018901
[8] Liu J G, Yang G Y, Hu Z L 2014 PLoS One 9 e89746
[9] Pei W D, Xia W, Wang Q L, et al. 2010 J. Univ. Sci. Technol. China 40 1186 (in Chinese) [裴伟东, 夏玮, 王全来 等 2010 中国科学技术大学学报 40 1186]
[10] Sorrentino F 2012 New J. Phys. 14 033035
[11] Wu Z Y, Duan J Q, Fu X C 2014 Appl. Math. Model 38 2961
[12] Krawiecki A 2014 Chaos, Soliton. Fract. 65 44
[13] Gmez S, Daz-Guilera A, Gmez-Gardees J, Prez-Vicente C J, Moreno Y, Arenas A 2013 Phys. Rev. Lett. 110 028701
[14] Wang J P, G Q, Yang G Y, Liu J G 2015 Physica A 428 250
[15] Yang G Y, Hu Z L, Liu J G 2015 Physica A 419 429
[16] Sol-Ribalta A, Domenico de M, Gmez S, Arenas A 2013 arXiv preprint arXiv:1506.07165 [physics.soc-ph]
[17] Buldyrev S V, Parshani R, Paul G, Stanley H E, Havlin S 2010 Nature 464 1025
[18] Dong G G, Gao J X, Du R J, Tian L X, Stanley H E, Havlin S 2013 Phys. Rev. E 87 052804
[19] Dong G G, Tian L X, Zhou D, Du R J, Xiao J, Stanley H E 2013 Euro. Lett. 102 68004
[20] Dong G G, Tian L X, Du R J, Stanley H E 2014 Physica A 394 370
[21] Segovia-Juarez J L, Colombano S, Kirschner D 2007 Biosystems 87 117
[22] Akram M, Dudek W A 2013 Inform. Sci. 218 182
[23] Rangasamy P, Akram M, Thilagavathi S 2013 Inform. Process. Lett. 113 599
[24] Segovia-Juarez J L, Colombano S 2003 BioSystems 68 187
[25] Berge C, Minieka E 1973 Graph and Hypergraph (North Holland: North-Holland Publishing Company Amsterdam) pp389-413
[26] Berge C, Sterboul F 1977 J. Comb. Theory B 22 97
[27] Estrada E, Rodrguez-Velzquez J A 2006 Physica A 364 581
[28] Volpentesta, A P 2008 Eur. J. Oper. Res. 188 390
[29] Pretolani D 2013 Eur. J. Oper. Res. 230 226
[30] Ghosal G, Zlatić V, Caldarelli G, Newman M E J 2009 Phys. Rev. E 79 066118
[31] Zlatić V, Ghoshal G, Caldarelli G 2009 Phys. Rev. E 80 036118
[32] Neubauer N, Obermayer K 2009 HT 09 Torino, Italy, June 29-July 1, 2009
[33] Bretto A 2013 Hypergraph Theory: An Introduction (New York: Springer Science Business Media)
[34] Peng X Z, Yao H, Du J, Wang Z, Ding C 2015 Acta Phys. Sin. 64 048901 (in Chinese) [彭兴钊, 姚宏, 杜军, 王哲, 丁超 2015 物理学报 64 048901]
[35] Chen S M, L H, Xu Q G, Xu Y F, Lai Q 2015 Acta Phys. Sin. 64 048902 (in Chinese) [陈世明, 吕辉, 徐青刚, 许云飞, 赖强 2015 物理学报 64 048902]
[36] Ding L, Zhang S Y 2012 Comput. Sci. 39 8 (in Chinese) [丁琳, 张嗣瀛 2012 计算机科学 39 8]
[37] Kanoko K 1992 Couple Map Lattice (Singapore: World Scientific)
[38] Wang X F, Xu J 2004 Phys. Rev. E 70 056113
[39] Xu J, Wang X F 2005 Physica A 349 685
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