COMPLEX NETWORKS MODELED ON A KIND OF SIERPIŃSKI-LIKE CARPET

Liang Huang and Li Peng
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Liang Huang: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China†School of Information and Mathematics, Yangtze University, Jingzhou 434023, P. R. China
Li Peng: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 03, 1-11

Abstract: In this paper, we use a kind of Sierpiński-like carpet to construct a special evolving network, whose nodes are all the solid squares in the construction of the carpet up to stage t. In our network, two nodes are neighbors if and only if the intersection of their corresponding squares is a line segment. Using the encoding method in fractal geometry, we show that our evolving network is scale-free and has the small-world effect, but is not fractal scaling.

Keywords: Complex Network; Sierpiński Carpet; Self-Similarity; Scale-Free; Small-World (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22500591

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