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

被引：15

作者：

Cheng, Kun ^{[1
]}

Chen, Dirong ^{[1
]}

Xue, Yumei ^{[1
]}

Zhang, Qian ^{[1
]}

机构：

[1] Beihang Univ, Sch Math Sci, Beijing 100083, Peoples R China

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2020年 / 28卷 / 03期

基金：

国家重点研发计划;

关键词：

Fractal; Sierpinski-Type Hexagon; Complex Network; Self-Similarity;

D O I：

10.1142/S0218348X20500541

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：12

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