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This paper proposes a unified model for hypernetworks and complex networks, and studies the evolution mechanisms of scale-free hypernetworks and the topological properties of the hypernetwork. We have analyzed the proposed model and calculated the stationary average hyperdegree distribution of the hypernetwork by using a Poisson process theory and a continuous technique. The analytical result agrees well with the simulation. It is shown that the hyperdegree distribution of the dynamic model follows a scale-free law. This paper not only integrates the hypernetwork model, in which one new node forms an edge with some old nodes, and the hypernetwork model, in which some new nodes form an edge with one old node, but also integrates the scale-free model in complex networks.
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Keywords:
- complex network /
- hypergraph /
- hypernetwork /
- scale-free
[1] Guo J L 2013 Evolving models of complex networks and human behavior dynamics (Beijing: Science Press) (in Chinese) [郭进利 2013 复杂网络和人类行为动力学演化模型(北京: 科学出版社)]
[2] Qi Y H, Guo J L 2013 University of Shanghai for Science and Technology 35 227 (in Chinese) [漆玉虎, 郭进利 2013 上海理工大学学报 35 227]
[3] Wang Y Z, Jin X L, Cheng X Q 2013 Chinese Journal of Computer 36 1125 (in Chinese) [王元卓, 靳小龙, 程学旗 2013 计算机学报 36 1125]
[4] Yin S, Ding S X, Haghani A, Hao H Y, Zhang P 2012 Journal of Process Control 22 1567
[5] Yin S, Luo H, Ding S X 2014 IEEE Trans.Ind.Electron. 61 2402
[6] Fang J Q 2013 Chinese Journal of Nature 35 345 (in Chinese) [方锦清 2013 自然杂志 35 345]
[7] Guo J L 2010 Chin. Phys. B 19 120503
[8] Guo J L, Guo Z H, Liu X J 2011 Chin. Phys. B 20 118902
[9] 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, 何佳倍, 李发旭, 李淑玲, 张子柯 2013 62 198901]
[10] Zhang Z K, Liu C 2010 J. Stat. Mech. 10005
[11] Wang J W, Rong L L, Deng Q H, Zhang J Y 2010 Eur. Phys. J. B 77 493
[12] 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]
[13] Yang G Y, Liu J G 2014 Chin. Phys. B 23 018901
[14] Denning P J 1985 American Scientist 73 127
[15] Nagurney A, Dong J 2002 Supernetworks: Decision- Making for the Information Age (Cheotenham: Edward Elgar Publishers)
[16] Nagurney A, Dong J, Zhang D 2002 Transportation Research E 38 281
[17] Wang Z T 2011 J. University of Shanghai for Science and Technology 33 229 (in Chinese) [王众托 2011 上海理工大学学报 33 229]
[18] Berge C 1973 Graphs and Hypergraphs (New York: Elsevier)
[19] Estrada E, Rodrigues V R 2005 Phys. Rev. E 71 1
[20] Estrada E, Rodrigues V R 2006 Physical A 364 581
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[1] Guo J L 2013 Evolving models of complex networks and human behavior dynamics (Beijing: Science Press) (in Chinese) [郭进利 2013 复杂网络和人类行为动力学演化模型(北京: 科学出版社)]
[2] Qi Y H, Guo J L 2013 University of Shanghai for Science and Technology 35 227 (in Chinese) [漆玉虎, 郭进利 2013 上海理工大学学报 35 227]
[3] Wang Y Z, Jin X L, Cheng X Q 2013 Chinese Journal of Computer 36 1125 (in Chinese) [王元卓, 靳小龙, 程学旗 2013 计算机学报 36 1125]
[4] Yin S, Ding S X, Haghani A, Hao H Y, Zhang P 2012 Journal of Process Control 22 1567
[5] Yin S, Luo H, Ding S X 2014 IEEE Trans.Ind.Electron. 61 2402
[6] Fang J Q 2013 Chinese Journal of Nature 35 345 (in Chinese) [方锦清 2013 自然杂志 35 345]
[7] Guo J L 2010 Chin. Phys. B 19 120503
[8] Guo J L, Guo Z H, Liu X J 2011 Chin. Phys. B 20 118902
[9] 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, 何佳倍, 李发旭, 李淑玲, 张子柯 2013 62 198901]
[10] Zhang Z K, Liu C 2010 J. Stat. Mech. 10005
[11] Wang J W, Rong L L, Deng Q H, Zhang J Y 2010 Eur. Phys. J. B 77 493
[12] 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]
[13] Yang G Y, Liu J G 2014 Chin. Phys. B 23 018901
[14] Denning P J 1985 American Scientist 73 127
[15] Nagurney A, Dong J 2002 Supernetworks: Decision- Making for the Information Age (Cheotenham: Edward Elgar Publishers)
[16] Nagurney A, Dong J, Zhang D 2002 Transportation Research E 38 281
[17] Wang Z T 2011 J. University of Shanghai for Science and Technology 33 229 (in Chinese) [王众托 2011 上海理工大学学报 33 229]
[18] Berge C 1973 Graphs and Hypergraphs (New York: Elsevier)
[19] Estrada E, Rodrigues V R 2005 Phys. Rev. E 71 1
[20] Estrada E, Rodrigues V R 2006 Physical A 364 581
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