Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (5): 1313-1321.

• Articles • Previous Articles     Next Articles

The Mathematical Foundation of the BA Model

 HOU Zhen-Ting, KONG Xiang-Xing, SHI Ding-Hua, CHEN Guan-Rong   

  1. School of Mathematics, Central South University, Changsha |410075;School of Mathematics, Central South University, Changsha |410075;Department of Mathematics, Shanghai University, Shanghai 200444;Department of Electronic Engineering, City University of Hong Kong, Hong Kong
  • Received:2010-08-31 Revised:2010-09-18 Online:2010-10-25 Published:2010-10-25
  • Supported by:

    国家自然科学基金(11071258)、湖南省研究生科研创新项目(CX2009B020)和中南大学研究生学位论文创新基金(2009ybfz11)资助

Abstract:

Based on the concept and techniques of Markov chain, this letter provides a rigorous proof for the existence of the steady-state degree distribution of the scale-free network generated by the Barabàsi-Albert (BA) model, and mathematically re-derives the exact analytic formulas of the distribution. The approach developed here is quite general, applicable to many other scale-free types of complex networks.

Key words: BA model, Scale-free network, Degree distribution, Markov chain

CLC Number: 

  • 05C80
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