REN Xue-Zao1, YANG Zi-Mo2, WANG Bing-Hong1,3, ZHOU Tao2,3**
1School of Science, Southwest University of Science and Technology, Mianyang 621010 2Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054 3Department of Modern Physics, University of Science and Technology of China, Hefei 230026
Mandelbrot Law of Evolving Networks
REN Xue-Zao1, YANG Zi-Mo2, WANG Bing-Hong1,3, ZHOU Tao2,3**
1School of Science, Southwest University of Science and Technology, Mianyang 621010 2Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054 3Department of Modern Physics, University of Science and Technology of China, Hefei 230026
摘要We show that the degree distribution of a growing network with linear preferential attachment approximately follows the Mandelbrot law, and propose an analytical method based on a recursive formula that can be used to obtain a more accurate expression of the shifting coefficient. Simulations demonstrate the advantages of our method. This work provides a possible mechanism leading to the Mandelbrot law of evolving networks, and refines the mainstream analytical methods for the shifting coefficient.
Abstract：We show that the degree distribution of a growing network with linear preferential attachment approximately follows the Mandelbrot law, and propose an analytical method based on a recursive formula that can be used to obtain a more accurate expression of the shifting coefficient. Simulations demonstrate the advantages of our method. This work provides a possible mechanism leading to the Mandelbrot law of evolving networks, and refines the mainstream analytical methods for the shifting coefficient.
(Probability theory, stochastic processes, and statistics)
引用本文:
REN Xue-Zao1, YANG Zi-Mo2, WANG Bing-Hong1,3, ZHOU Tao2,3**. Mandelbrot Law of Evolving Networks[J]. 中国物理快报, 2012, 29(3): 38904-038904.
REN Xue-Zao, YANG Zi-Mo, WANG Bing-Hong, ZHOU Tao. Mandelbrot Law of Evolving Networks. Chin. Phys. Lett., 2012, 29(3): 38904-038904.
[1] Strogatz S H 2001 Nature 410 268
[2] Dorogovtsev S N 2002 Adv. Phys. 51 1079
[3] Albert R and Barabási A L 2002 Rev. Mod. Phys. 74 47
[4] Newman M E J 2003 SIAM Rev. 167 45
[5] Watts D J and Strogatz S H 1998 Nature 393 440
[6] Barabási A L and Albert R 1999 Science 286 509
[7] Barabási A L, Albert R and Jeong H 1999 Physica A 272 173
[8] Newman M E J 2005 Comtemporary Physics 46 323
[9] Clauset A, Shalizi C R and Newman M E J 2009 SIAM Rev. 51 661
[10] Newman M E J 2001 Proc. Natl. Acad. Sci. U. S.A. 98 404
[11] Newman M E J, Forrest S and Balthrop J 2002 Phys. Rev. E 66 035101
[12] Zhang P P, Chen K, He Y, Zhou T, Su B B, Jin Y D, Chang H, Zhou Y P, Sun L C, Wang B H and He D R 2006 Physica A 360 599
[13] Shang M S, Lü L, Zhang Y C and Zhou T 2010 Eur. Phys. Lett. 90 48006
[14] Li W and Cai X 2004 Phys. Rev. E 69 046106
[15] Liu H K and Zhou T 2007 Acta Phys. Sin. 56 106 (in Chinese)
[16] Bagler G 2008 Physica A 387 2972
[17] Mandelbrot B 1965 Information Theory and Psycholinguistics (New York: Basic Books Publishing Co.)
[18] Dorogovtsev S N, Mendes J F F and Samukhin A N 2000 Phys. Rev. Lett. 85 4633
[19] Chang H, Su B B, Zhou Y P and He D R 2007 Physica A 383 687
[20] Wang Y L, Zhou T, Shi J J, Wang J and He D R 2009 Physica A 388 2949
[21] Leskovec J, Kleinberg J and Faloutsos C 2007 ACM Trans. Knowl. Disc. from Data 1 1
[22] Jeong H, Mason S, Barabási A L and Oltvai Z N 2001 Nature 411 41
[23] Kunegis J, Lommatzsch A and Bauckhage C 2009 Proc. 18th Intl. Conf. WWW (New York: ACM Press)
[24] Colizza V, Pastor Satorras R and Vespignani A 2007 Nature Phys. 3 276
[25] Opsahl T and Panzarasa P 2009 Social Networks 31 155
[26] Krapivsky P L, Redner S and Leyvraz F 2000 Phys. Rev. Lett. 85 4629
[27] Zhou T, Yan G and Wang B H 2005 Phys. Rev. E 71 046141
[28] Moore C, Ghoshal G and Newman M E J 2006 Phys. Rev. E 74 036121
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