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Analyses Of Some Structural Properties On A Class Of Hierarchical Scale-Free Networks

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  • JIA-BAO LIU

    (School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, P. R. China)

  • YAN BAO

    (School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, P. R. China)

  • WU-TING ZHENG

    (School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, P. R. China)

Abstract

Hierarchical networks as fundamental models to describe the complex networks, have many applications in networks science, engineering technology and so on. In this paper, we first propose a new class of hierarchical networks with fractal structure, which are the networks with triangles compared to traditional hierarchical networks. Second, we study the precise results of some structural properties to derive small-world effect and scale-free feature. Third, it is found that the constructed network is sparse through the average degree and density. Fourth, it is also demonstrated that the degree distributions of hub nodes and the bottom nodes are the power law and exponential, respectively. Finally, we prove that clustering coefficient with a definite value z tends to stabilize at a lower bound as t iterates to a certain number, and the average distance of Gtz has an increasing relationship along with the value of ln Nt.

Suggested Citation

  • Jia-Bao Liu & Yan Bao & Wu-Ting Zheng, 2022. "Analyses Of Some Structural Properties On A Class Of Hierarchical Scale-Free Networks," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(07), pages 1-11, November.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:07:n:s0218348x22501365
    DOI: 10.1142/S0218348X22501365
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    Cited by:

    1. Yu Gao, 2023. "RETRACTED ARTICLE: AISAS model-based statistical analysis for intelligent eldercare products consumption research," Journal of Combinatorial Optimization, Springer, vol. 45(5), pages 1-16, July.
    2. Jia-Bao Liu & Xin-Bei Peng & Jing Zhao, 2023. "Analyzing the spatial association of household consumption carbon emission structure based on social network," Journal of Combinatorial Optimization, Springer, vol. 45(2), pages 1-34, March.
    3. Cheng-Ben Wang & Qian Zhong, 2023. "RETRACTED ARTICLE: International market risk, monetary policy stance, and corporate financing: China’s economic recovery in the post-pandemic era," Journal of Combinatorial Optimization, Springer, vol. 46(1), pages 1-37, August.
    4. Zhanfeng Wang & Lisha Yao & Xiaoyu Shao & Honghai Wang, 2023. "RETRACTED ARTICLE: A combination of TEXTCNN model and Bayesian classifier for microblog sentiment analysis," Journal of Combinatorial Optimization, Springer, vol. 45(4), pages 1-22, May.
    5. Xinglong Chang & Jianrong Wang & Rui Guo & Yingkui Wang & Weihao Li, 2023. "Asymmetric Graph Contrastive Learning," Mathematics, MDPI, vol. 11(21), pages 1-13, October.

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