A Small-World Model of Scale-Free Networks: Features and Verifications

Abstract:

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It is now well known that many large-sized complex networks obey a scale-free power-law vertex-degree distribution. Here, we show that when the vertex degrees of a large-sized network follow a scale-free power-law distribution with exponent  2, the number of degree-1 vertices, if nonzero, is of order N and the average degree is of order lower than log N, where N is the size of the network. Furthermore, we show that the number of degree-1 vertices is divisible by the least common multiple of , , . . ., , and l is less than log N, where l = < is the vertex-degree sequence of the network. The method we developed here relies only on a static condition, which can be easily verified, and we have verified it by a large number of real complex networks.

Info:

Periodical:

Edited by:

Shaobo Zhong, Yimin Cheng and Xilong Qu

Pages:

166-170

DOI:

10.4028/www.scientific.net/AMM.50-51.166

Citation:

W. J. Xiao et al., "A Small-World Model of Scale-Free Networks: Features and Verifications", Applied Mechanics and Materials, Vols. 50-51, pp. 166-170, 2011

Online since:

February 2011

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Price:

$35.00

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