Power-Law Exponent for Exponential Growth Network
WANG Li-Na1,2 , CHEN Bin1** , ZANG Chen-Rui3
1 Business School, University of Shanghai for Science and Technology, Shanghai 200093 2 College of Sciences, Inner Mongolian University of Technology, Hohhot 010051 3 China Unicom Inner Mongolian Branch, Hohhot 010020
Abstract :The question of the power-law exponent of exponential growth networks is studied here. In a discrete case, the degree distribution is defined as the probability distribution of the discrete variable. Based on this, the degree distribution of the pseudofractal scale-free web, an exponential growth network, is obtained. The power-law exponent ln3/ln2 is analyzed according to the maximum likelihood principle. It satisfies consistency and is good for small generations of the network. For many exponential growth networks, their power-law exponent needs to be tested. The work provides a new view on the power-law exponent of an exponential growth network.
收稿日期: 2012-04-06
出版日期: 2012-07-31
[1] Dorogovtsev S N, Goltsev A V and Mendes J F F 2002 Phys. Rev. E 65 066122 [2] Jung S, Kim S and Kahng B 2002 Phys. Rev. E 65 056101 [3] Noh J D 2003 Phys. Rev. E 67 045103 [4] Comellas F, Fertin G and Raspaud A 2004 Phys. Rev. E 69 037104 [5] Andrade J S, Herrmann H J, Andrade R F S and da Silva L R 2005 Phys. Rev. Lett. 94 018702 [6] Soares D J B, Andrade J S, Herrmann H J and da Silva L R 2006 Int. J. Mod. Phys. C 17 1219 [7] Zhang Z Z, Rong L L and Zhou S G 2007 Physica A 377 329 [8] Zhang Z Z, Rong L L and Comellas F 2006 Physica A 364 610 [9] Zhang Z Z, Rong L L and Zhou S G 2006 Phys. Rev. E 74 046105 [10] Andrade J S, Herrmann H J, Andrade R F S and da Silva L R 2009 Phys. Rev. Lett. 102 079901 [11] Guo J L and Wang L N 2010 Phys. Procedia 3 1791 [12] Mungan M 2011 Phys. Rev. Lett. 106 029802 [13] Ravasz E and Barabási A L 2003 Phys. Rev. E 67 026112 [14] Barabási A L, Ravasz E and Vicsek T 2001 Physica A 299 559 [15] Nacher J C, Ueda N, Kanehisa M and Akutsu T 2005 Phys. Rev. E 71 036132 [16] Zhang Z Z, Rong L L and Guo C H 2006 Physica A 363 567 [17] Zhang Z Z, Comellas F, Fertin G and Rong L L 2006 J. Phys. A: Math. Gen. 39 1811 [18] Zhang Z Z, Qi Y, Zhou S G, Xie W L and Guan J H 2009 Phys. Rev. E 79 021127 [19] Agliari E and Burioni R 2009 Phys. Rev. E 80 031125 [20] Zhang Y C, Zhang Z Z, Zhou S G and Guan J H 2010 Physica A 389 3316 [21] Zhou T, Yan G and Wang B H 2005 Phys. Rev. E 71 046141 [22] Vieira A P, Andrade J S, Herrmann H J and Andrade R F S 2007 Phys. Rev. E 76 26111 [23] Auto D M, Moreira A A, Herrmann H J and Andrade J S 2008 Phys. Rev. E 78 066112 [24] Moreira A A, Paula D R, Filho R N C and Andrade J S 2006 Phys. Rev. E 73 65101 [25] Lind P G, da Silva L R, Andrade J S and Herrmann H J 2007 Europhys. Lett. 78 68005 [26] de Oliveira I N, de Moura F A B F, Lyra M L, Andrade J S and Albuquerque E L 2009 Phys. Rev. E 79 16104 [27] Dorogovtsev S N, Goltsev A V and Mendes J F F 2008 Rev. Mod. Phys. 80 1275 [28] Song C, Havlin S and Makse H A 2005 Nature 433 392 [29] Song C, Havlin S and Makse H A 2006 Nature Phys. 2 275 [30] Adamic L A and Huberman B A 2002 Glottometrics 3 143 [31] Adamic L A 2000 http://www.hpl.hp.com/research/idl/papers/ranking [32] Albert R and Barabási A -L 2002 Rev. Mod. Phys. 74 47 [33] Albert R 2006 LACUS Forum 32: Network ed Hwang S J, Sullivan W J and Lommel A R (Houston: Linguistic Association of Canada and the United States) pp 5–20 [34] Thadakamalla H P, Kumara S R T and Albert R 2007 Operations Research Management Science Handbook ed Ravindran A R (Boca Raton FL: CRC press) chap 11 pp 1–59 [35] Barabási A -L 2007 IEEE Control Syst. Mag. 27 33 [36] Dorogovtsev S N 2010 Lectures Complex Networks (New York: Oxford University Press) pp 1–8 [37] Clauset A, Shalizi C R and Newman M E J 2009 SIAM Rev. 51 661 [38] Newey W K and Mcfadden D L 1994 Handbook Econometrics ed Engle R F and Mcfadden D L (North Holland: Elsevier) vol 4 pp 2113–2235 [39] Wang L N, Chen B and Yan Z Z 2011 Phys. Lett. A 375 2533
[1]
. [J]. 中国物理快报, 2022, 39(8): 80503-080503.
[2]
. [J]. 中国物理快报, 2017, 34(6): 68901-.
[3]
. [J]. 中国物理快报, 2017, 34(5): 58902-.
[4]
. [J]. 中国物理快报, 2016, 33(10): 108901-108901.
[5]
. [J]. 中国物理快报, 2016, 33(06): 68901-068901.
[6]
. [J]. 中国物理快报, 2015, 32(12): 128901-128901.
[7]
. [J]. 中国物理快报, 2015, 32(03): 30501-030501.
[8]
. [J]. Chin. Phys. Lett., 2013, 30(3): 38901-038901.
[9]
LI Ling**;JIN Zhen-Lan
. Scale-Free Brain Networks Based on the Event-Related Potential during Visual Spatial Attention [J]. 中国物理快报, 2011, 28(4): 48701-048701.
[10]
ZHANG Jiang**;WANG You-Gui
. Size Dependency of Income Distribution and Its Implications [J]. 中国物理快报, 2011, 28(3): 38901-038901.
[11]
ZOU Sheng-Rong;XU Ying-Ying;XU Xiu-Lian;WANG Jian;HE Da-Ren**
. A Simple Model of Interaction between Journals, Authors and Editorial Board Members [J]. 中国物理快报, 2011, 28(1): 18902-018902.
[12]
XU Yan;GUO Liang-Peng;DING Ning;WANG You-Gui. Evidence of Scaling in Chinese Income Distribution [J]. 中国物理快报, 2010, 27(7): 78901-078901.
[13]
LIU Jian-Ye;;GUO Wen-Jun. Finding a Probe for Extracting Information on the Momentum Dependent-Interaction in Heavy Ion Collisions [J]. 中国物理快报, 2010, 27(6): 62503-062503.
[14]
ZHU Jun-Fang;HAN Xiao-Pu;WANG Bing-Hong;. Statistical Property and Model for the Inter-Event Time of Terrorism Attacks [J]. 中国物理快报, 2010, 27(6): 68902-068902.
[15]
SHANG Ming-Sheng;CHEN Guan-Xiong;DAI Shuang-Xing;WANG Bing-Hong;ZHOU Tao;. Interest-Driven Model for Human Dynamics [J]. 中国物理快报, 2010, 27(4): 48701-048701.