RANDOM CONTINUOUS MODEL OF SCALE-FREE NETWORKS

Xianmin GENG

系统科学与复杂性(英文) ›› 2011, Vol. 24 ›› Issue (2) : 218-224.

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PDF(159 KB)
系统科学与复杂性(英文) ›› 2011, Vol. 24 ›› Issue (2) : 218-224. DOI: 10.1007/s11424-011-8076-6
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RANDOM CONTINUOUS MODEL OF SCALE-FREE NETWORKS

    Xianmin GENG
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RANDOM CONTINUOUS MODEL OF SCALE-FREE NETWORKS

    Xianmin GENG
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摘要

There are a lot of continuous evolving networks in real world, such as Internet, WWW network, etc. The evolving operation of these networks are not an equating
interval of time by chance. In this paper, the author proposes a new mathematical model for the mechanism of continuous single preferential attachment on the scale free networks, and counts the distribution of degree using stochastic analysis. Namely, the author has established the random continuous model of the network evolution of which counting process determines the operating number, and has
proved that this system self-organizes into scale-free structures with scaling exponent γ=3+αm.

Abstract

There are a lot of continuous evolving networks in real world, such as Internet, WWW network, etc. The evolving operation of these networks are not an equating
interval of time by chance. In this paper, the author proposes a new mathematical model for the mechanism of continuous single preferential attachment on the scale free networks, and counts the distribution of degree using stochastic analysis. Namely, the author has established the random continuous model of the network evolution of which counting process determines the operating number, and has
proved that this system self-organizes into scale-free structures with scaling exponent γ=3+αm.

关键词

Counting processes / degree distribution / scaling exponent / scale-free networks.

Key words

Counting processes / degree distribution / scaling exponent / scale-free networks.

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Xianmin GENG. RANDOM CONTINUOUS MODEL OF SCALE-FREE NETWORKS. 系统科学与复杂性(英文), 2011, 24(2): 218-224 https://doi.org/10.1007/s11424-011-8076-6
Xianmin GENG. RANDOM CONTINUOUS MODEL OF SCALE-FREE NETWORKS. Journal of Systems Science and Complexity, 2011, 24(2): 218-224 https://doi.org/10.1007/s11424-011-8076-6
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