Degree distributions and motif profiles of Thue–Morse complex network

Xiaohua Hu and Min Niu

Chaos, Solitons & Fractals, 2023, vol. 176, issue C

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.

Keywords: Thue–Morse sequence; Horizontal visibility graph; Degree distribution; Sequential 4-node motifs (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:176:y:2023:i:c:s0960077923010421

DOI: 10.1016/j.chaos.2023.114141

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