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Degree Distribution of a Scale-free Random Graph Model

Degree Distribution of a Scale-free Random Graph Model
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摘要 In this paper, we consider the degree distribution of a general random graph with multiple edges and loops from the perspective of probability. Based on the first-passage probability of Markov chains, we give a new and rigorous proof to the existence of the network degree distribution and obtain the precise expression of the degree distribution. The analytical results are in good agreement with numerical simulations. In this paper, we consider the degree distribution of a general random graph with multiple edges and loops from the perspective of probability. Based on the first-passage probability of Markov chains, we give a new and rigorous proof to the existence of the network degree distribution and obtain the precise expression of the degree distribution. The analytical results are in good agreement with numerical simulations.
作者 Li TAN Zhen Ting HOU Xin Ru LIU
机构地区 School of Mathematics School of Traffic and Transportation Engineering
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第3期587-598,共12页 数学学报（英文版）
基金 Supported by National Natural Science Foundation of China (Grant Nos. 10671212, 90820302)
关键词 Degree distribution SCALE-FREE Markov chains Degree distribution, scale-free, Markov chains
分类号 O157.5 [理学—基础数学] N941.4 [自然科学总论—系统科学]
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参考文献15

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  • 2Barabasi, A. L., Albert, R.: Emergence of scaling in random networks. Science, 286, 509-512 (1999).
  • 3Albert, R., Jeong, H., Barabasi, A. L.: Diameter of the world-wide web. Nature, 401, 130-131 (1999).
  • 4Barabasi, A. L., Albert, R., Jeong, H.: Mean-field theory for scale-free random networks. Physics A, 272, 173-187 (1999).
  • 5Krapivsky, P. L., Redner, S., Leyvraz, F.: Connectivity of growing random networks. Phys. Rev. Left., 85, 4629-4632 (2000).
  • 6Dorogovtsev, S. N., Mendes, J. F. F., Samukhin, A. N.: Structure of growing networks with preferential linking. Phys. Rev. Lett., 85, 4633-4636 (2000).
  • 7Jordan, J.: The degree sequence and spectra of scale-free random graphs. Random Structures and Algo- rithms, 29, 226-242 (2006).
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Acta Mathematica Sinica,English Series
2012年 第3期

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