# 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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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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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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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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