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The visibility graph of n-bonacci sequence

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  • Bai, Shiwei
  • Niu, Min

Abstract

In this paper, we study both the visibility graph and horizontal visibility graph of n-bonacci sequence. Firstly, we map Fibonacci sequence to complex network by using visibility graph algorithm, and its degree sequence is related to some combinatorial properties of words. Then, we study the visibility graph degree distribution of n-bonacci sequence by coding words. We obtain that its degree distribution is between the exponential and power-law distributions. On the other hand, the horizontal visibility graph sequences of n-bonacci sequence over different alphabets correspond to the same n-bonacci sequence, and its degree distribution tends to exponential distribution as n→∞. Finally, we explain the reason why fractal sequences are mapped into scale-free networks.

Suggested Citation

  • Bai, Shiwei & Niu, Min, 2022. "The visibility graph of n-bonacci sequence," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    • Handle: RePEc:eee:chsofr:v:163:y:2022:i:c:s0960077922007056
    DOI: 10.1016/j.chaos.2022.112500
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    References listed on IDEAS

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    1. Lucas Lacasa & Ryan Flanagan, 2016. "Irreversibility of financial time series: a graph-theoretical approach," Papers 1601.01980, arXiv.org.
    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. Gutin, Gregory & Mansour, Toufik & Severini, Simone, 2011. "A characterization of horizontal visibility graphs and combinatorics on words," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2421-2428.
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    Cited by:

    1. Hu, Xiaohua & Niu, Min, 2023. "Degree distributions and motif profiles of Thue–Morse complex network," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    2. Bai, Shiwei & Niu, Min & Wang, Yu, 2024. "The network structure of Sturmian sequences based on HVG," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 634(C).
    3. Hu, Xiaohua & Niu, Min, 2023. "Horizontal visibility graphs mapped from multifractal trinomial measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    4. Liu, Jin-Long & Yu, Zu-Guo & Zhou, Yu, 2024. "A cross horizontal visibility graph algorithm to explore associations between two time series," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

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