Emergence of scaling in non-uniform hypernetworksdoes the rich get richer lead to a power-law distribution?

Guo Jin-Li

doi:10.7498/aps.63.208901

Abstract

In this paper, we propose a hypernetwork model with a nonlinear preferential attachment, and study the evolving mechanism and topological properties of the hypernetwork. We analyze the model by using a Poisson process theory and a continuous technique, and give a characteristic equation of hyperdegrees. We obtain the stationary average hyperdegree distribution of the hypernetwork by the characteristic equation. The analytical result shows that the hypernetwork has a phenomenon of the rich get richer, and it accords well with the simulation. It is shown in this paper that the hyperdegree distribution of the dynamic model exhibits a stretched exponential distribution with the increase of the hypernetwork size. It proves that the rich get richer does not necessarily induce a power-law distribution.

Keywords:

Authors and contacts

Guo Jin-Li^{1 2}

1.
Business School, University of Shanghai for Science and Technology, Shanghai 200093, China;
2.
Center for Supernetwork Research, University of Shanghai for Science and Technology, Shanghai 200093, China
Funds: Project supported by the Hujiang Foundation of China (Grant No. A14006) and the Shanghai First-class Academic Discipline Project, China (Grant No. S1201YLXK).

References

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[7]	Yin S, Wang G, Karimi H R 2014 Mechatronics 24 289
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[15]	Wang J W, Rong L L, Deng Q H, Zhang J Y 2010 Eur. Phys. J. B 77 493
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[17]	Wu Z Y, Duan J Q, Fu X C 2014 Appl. Math. Model. 38 2961
[18]	Yang G Y, Liu J G 2014 Chin. Phys. B 23 018901
[19]	Guo J L, Zhu X Y 2014 Acta Phys. Sin. 63 090207 (in Chinese) [郭进利, 祝昕昀 2014 物理学报 63 090207]
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[21]	Nagurney A, Dong J 2002 Supernetworks: Decision-Making for the Information Age (Cheotenham: Edward Elgar Publishers)
[22]	Wang Z T 2011 J. Univ. Shanghai Sci. Technol. 33 229 (in Chinese) [王众托 2011 上海理工大学学报 33 229]
[23]	Berge C 1973 Graphs and Hypergraphs (2nd Ed.) (New York: Elsevier) 389
[24]	Estrada E, Juan A, Rodríguez V 2006 Physica A 364 581
[25]	Krapivsky P L, Redner S, Leyvraz F 2000 Phys. Rev. Lett. 85 4629

Cited By

[1]	Wang Z P, Wang Z T 2008 Hypernetwork Theory and Application (Beijing: Science Press) (in Chinese) [王志平, 王众托 2008 超网络理论及其应用 (北京: 科学出版社)]
[2]	Qi Y H, Guo J L 2013 J. Univ. Shanghai Sci. Technol. 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 Chin. J. Comput. 36 1125 (in Chinese) [王元卓, 靳小龙, 程学旗 2013 计算机学报 36 1125]
[4]	Guo H D, Wang L Z, Chen F, Liang D 2014 Chin. Sci. Bull. 59 1047 (in Chinese) [郭华东,王力哲, 陈方, 梁栋 2014 科学通报 59 1047]
[5]	Yin S, Luo H, Ding S X 2014 IEEE Trans.Ind.Electron. 61 2402
[6]	Yin S, Ding S X, Sari A H A, Hao H Y 2013 Int. J. Syst. Sci. 44 1366
[7]	Yin S, Wang G, Karimi H R 2014 Mechatronics 24 289
[8]	Yin S, Yang X B, Karimi H R 2012 Math. Problems in Engineering 2012 1
[9]	Fang J Q 2013 Chin. J. Nature 35 345 (in Chinese) [方锦清 2013 自然杂志 35 345]
[10]	Frnkranz J, Hllermeier E, Higuchi T 2013 Lecture Notes in Computer Science (Verlag Berlin Heidelbeg: Springer) pp324-339
[11]	Kim S J, Ha J H, Zhang B T 2014 J. Biomed. Inform. 49 101
[12]	Ni Z J, Rong L L, Liu Q 2013 J. Manag. Sci. China 16 68 (in Chinese) [倪子建, 荣莉莉, 刘泉 2013 管理科学学报 16 68]
[13]	Zhang Z K, Liu C 2010 J. Stat. Mech. P10005
[14]	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 物理学报 62 198901]
[15]	Wang J W, Rong L L, Deng Q H, Zhang J Y 2010 Eur. Phys. J. B 77 493
[16]	Hu F, Zhao H X, Ma X J 2013 Sci. China G: Phys. Mech. Astron. 43 16 (in Chinese) [胡枫, 赵海兴, 马秀娟 2013 中国科学G辑: 物理学力学天文学 43 16]
[17]	Wu Z Y, Duan J Q, Fu X C 2014 Appl. Math. Model. 38 2961
[18]	Yang G Y, Liu J G 2014 Chin. Phys. B 23 018901
[19]	Guo J L, Zhu X Y 2014 Acta Phys. Sin. 63 090207 (in Chinese) [郭进利, 祝昕昀 2014 物理学报 63 090207]
[20]	Denning P J 1985 American Scientist 73 127
[21]	Nagurney A, Dong J 2002 Supernetworks: Decision-Making for the Information Age (Cheotenham: Edward Elgar Publishers)
[22]	Wang Z T 2011 J. Univ. Shanghai Sci. Technol. 33 229 (in Chinese) [王众托 2011 上海理工大学学报 33 229]
[23]	Berge C 1973 Graphs and Hypergraphs (2nd Ed.) (New York: Elsevier) 389
[24]	Estrada E, Juan A, Rodríguez V 2006 Physica A 364 581
[25]	Krapivsky P L, Redner S, Leyvraz F 2000 Phys. Rev. Lett. 85 4629

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Vol. 63, Issue 20 - 2014-10-20

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