## Abstract

An Horizontal Visibility Graph (for short, HVG) is defined in association with

an ordered set of non-negative reals. HVGs realize a methodology in the

analysis of time series, their degree distribution being a good discriminator

between randomness and chaos [B. Luque, \emph{et al.}, \emph{Phys. Rev. E}

\textbf{80} (2009), 046103]. We prove that a graph is an HVG if and only if

outerplanar and has a Hamilton path. Therefore, an HVG is a noncrossing graph,

as defined in algebraic combinatorics [P. Flajolet and M. Noy, \emph{Discrete

Math.}, \textbf{204} (1999) 203-229]. Our characterization of HVGs implies a

linear time recognition algorithm.\textbf{ }Treating ordered sets as words, we

characterize subfamilies of HVGs highlighting various connections with

combinatorial statistics and introducing the notion of a visible pair. With

this technique we determine asymptotically the average number of edges of HVGs.

an ordered set of non-negative reals. HVGs realize a methodology in the

analysis of time series, their degree distribution being a good discriminator

between randomness and chaos [B. Luque, \emph{et al.}, \emph{Phys. Rev. E}

\textbf{80} (2009), 046103]. We prove that a graph is an HVG if and only if

outerplanar and has a Hamilton path. Therefore, an HVG is a noncrossing graph,

as defined in algebraic combinatorics [P. Flajolet and M. Noy, \emph{Discrete

Math.}, \textbf{204} (1999) 203-229]. Our characterization of HVGs implies a

linear time recognition algorithm.\textbf{ }Treating ordered sets as words, we

characterize subfamilies of HVGs highlighting various connections with

combinatorial statistics and introducing the notion of a visible pair. With

this technique we determine asymptotically the average number of edges of HVGs.

Original language | English |
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Pages (from-to) | 2421-2428 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 390 |

Publication status | Published - 2011 |