• Corpus ID: 242757613

Counting Horizontal Visibility Graphs

@inproceedings{JuhnkeKubitzke2021CountingHV,
  title={Counting Horizontal Visibility Graphs},
  author={Martina Juhnke-Kubitzke and Daniel Kohne and Jonas Schmidt},
  year={2021}
}
Horizontal visibility graphs (HVGs, for short) are a common tool used in the analysis and classification of time series with applications in many scientific fields. In this article, extending previous work by Lacasa and Luque, we prove that HVGs associated to data sequences without equal entries are completely determined by their ordered degree sequence. Moreover, we show that HVGs for data sequences without and with equal entries are counted by the Catalan numbers and the large Schröder… 
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References

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Abstract Horizontal visibility graphs (HVGs) are graphs constructed in correspondence with number sequences that have been introduced and explored recently in the context of graph-theoretical time…
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TLDR
The proposed encoder/decoder approach offers an on-line computation solution at no additional computational cost, and makes it possible to use visibility graphs for large-scale time series analysis and for applications where on- line data assimilation is required.
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TLDR
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TLDR
This work presents the horizontal visibility algorithm, a geometrically simpler and analytically solvable version of the former algorithm, focusing on the mapping of random series (series of independent identically distributed random variables), and presents exact results on the topological properties of graphs associated with random series, namely, the degree distribution, the clustering coefficient, and the mean path length.
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A simple and fast computational method, the visibility algorithm, that converts a time series into a graph, which inherits several properties of the series in its structure, enhancing the fact that power law degree distributions are related to fractality.
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Sequences and arrays whose terms enumerate combinatorial structures have many applications in computer science. Knowledge (or estimation) of such integer-valued functions is, for example, needed in…
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TLDR
There exists a persistent graph G that is not the visibility graph for any terrain T, which implies that pseudo-terrains are not stretchable and persistence is not enough by itself to characterize the visibility graphs of terrains.
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