Acta mathematica scientia, Series B >
EXACT SOLUTION OF THE DEGREE DISTRIBUTION FOR AN EVOLVING NETWORK
Received date: 2008-12-25
Online published: 2009-05-20
Supported by
This research is supported by the National Natural Science Foundation of China (10671212), and Research Fund for the Doctoral Program of Higher Education of China (20050533036)
In this paper we propose a simple evolving network with link additions as well as removals. The preferential attachment of link additions is similar to BA model’s, while the removal rule is newly added. From the perspective of Markov chain, we give the exact solution of the degree distribution and show that whether the network is scale-free or not depends on the parameter m, and the degree exponent varying in (3, 5] is also depend on m if scale-free.
Key words： evolving networks; preferential attachmen; difference equation; power law
HOU Zhen-Ting , KONG Xiang-Xing . EXACT SOLUTION OF THE DEGREE DISTRIBUTION FOR AN EVOLVING NETWORK[J]. Acta mathematica scientia, Series B, 2009 , 29(3) : 723 -730 . DOI: 10.1016/S0252-9602(09)60067-9
[1] Barabási A, Albert R. Emergence of scaling in random networks. Science, 1999, 286: 509–512
[2] Newman M, Forrest S, Baldrop J. Email networks and the spread of computer viruses. Phys Rev E, 2002,
66: 035101
[3] Wang J, Wilde P. Properties of evolving e-mail networks. Phys Rev E, 200, 70: 066121
[4] Shi D, Liu L, Zhu S, et al. Degree distributions of evolving networks. Europhys Lett, 2006, 76: 731–737
[5] Stolz O. Vorlesungen uber allgemiene Arithmetic. Leipzig: Teubner, 1886
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