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Degree distributions and motif profiles of Thue–Morse complex network

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  • Hu, Xiaohua
  • Niu, Min

Abstract

In this paper, we study both the horizontal visibility graph (HVG) and the limited penetrable horizontal visibility graph (LPHVG) mapped from the Thue–Morse sequence. Firstly, we map the series to complex networks by using visibility graph algorithms. Then, we obtain the analytical degree distribution of the Thue–Morse HVG through an iterative method. And we also derive the degree distribution of the Thue–Morse LPHVG with a penetrable distance of ρ=1. Finally, we investigate the profile of sequential 4-node motifs for the Thue–Morse HVG. The relative frequencies of the 4-node motifs for the Thue–Morse HVG converge to a constant vector (12,16,16,16,0,0). The numerical simulations coincide excellently with theoretical results of the degree distributions and motif profiles.

Suggested Citation

  • Hu, Xiaohua & Niu, Min, 2023. "Degree distributions and motif profiles of Thue–Morse complex network," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:chsofr:v:176:y:2023:i:c:s0960077923010421
    DOI: 10.1016/j.chaos.2023.114141
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    References listed on IDEAS

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    1. Bai, Shiwei & Niu, Min, 2022. "The visibility graph of n-bonacci sequence," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    2. Li, Sange & Shang, Pengjian, 2021. "Analysis of nonlinear time series using discrete generalized past entropy based on amplitude difference distribution of horizontal visibility graph," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Xie, Wen-Jie & Zhou, Wei-Xing, 2011. "Horizontal visibility graphs transformed from fractional Brownian motions: Topological properties versus the Hurst index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3592-3601.
    4. Wang, Minggang & Xu, Hua & Tian, Lixin & Eugene Stanley, H., 2018. "Degree distributions and motif profiles of limited penetrable horizontal visibility graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 620-634.
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