ArticleScientific reports2018
Exact results of the limited penetrable horizontal visibility graph associated to random time series and its application.
Article in Scientific reports, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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Who cites it
3 citing papers in PubMed.
- Topological-spectral fusion of secondary acoustic echoes for identity recognition in non-line-of-sight environments.Scientific reports · 2026Article
- Six-sigma approach-based visibility graphs.Scientific reports · 2026Article
- Distinction of Chaos from Randomness Is Not Possible from the Degree Distribution of the Visibility and Phase Space Reconstruction Graphs.Entropy (Basel, Switzerland) · 2024Article
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Authors and funding
7 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
The limited penetrable horizontal visibility algorithm is an analysis tool that maps time series into complex networks and is a further development of the horizontal visibility algorithm. This paper presents exact results on the topological properties of the limited penetrable horizontal visibility graph associated with independent and identically distributed (i:i:d:) random series. We show that the i.i.d: random series maps on a limited penetrable horizontal visibility graph with exponential degree distribution, independent of the probability distribution from which the series was generated. We deduce the exact expressions of mean degree and clustering coefficient, demonstrate the long distance visibility property of the graph and perform numerical simulations to test the accuracy of our theoretical results. We then use the algorithm in several deterministic chaotic series, such as the logistic map, H´enon map, Lorenz system, energy price chaotic system and the real crude oil price. Our results show that the limited penetrable horizontal visibility algorithm is efficient to discriminate chaos from uncorrelated randomness and is able to measure the global evolution characteristics of the real time series.
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Registered trials
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