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THE SCALE-FREE AND SMALL-WORLD PROPERTIES OF COMPLEX NETWORKS ON SIERPINSKI-TYPE HEXAGON

KUN CHENG

School of Mathematical Sciences, Beihang University, Beijing 100083, P. R. China

E-mail Address: kuncstat@buaa.edu.cn

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DIRONG CHEN

School of Mathematical Sciences, Beihang University, Beijing 100083, P. R. China

E-mail Address: drchen@buaa.edu.cn

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YUMEI XUE

http://orcid.org/0000-0003-4872-6479

School of Mathematical Sciences, Beihang University, Beijing 100083, P. R. China

E-mail Address: yxue@buaa.edu.cn

Corresponding author.

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, and

QIAN ZHANG

School of Mathematical Sciences, Beihang University, Beijing 100083, P. R. China

E-mail Address: qianzh@buaa.edu.cn

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https://doi.org/10.1142/S0218348X20500541Cited by:13 (Source: Crossref)

Abstract

In this paper, a network is generated from a Sierpinski-type hexagon by applying the encoding method in fractal. The criterion of neighbor is established to quantify the relationships among the nodes in the network. Based on the self-similar structures, we verify the scale-free and small-world effects. The power-law exponent on degree distribution is derived to be ${log}_{2} 6$ and the average clustering coefficients are shown to be larger than $0.4255$ . Moreover, we give the bounds of the average path length of our proposed network from the renewal theorem and self-similarity.

Keywords:

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