2010/10/09 by Gregory Gutin, Toufik Mansour, Simone Severini · 3 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #physics.data-an
paper · pdf · doi:10.1016/j.physa.2011.02.031
published as Physica A: Statistical Mechanics and its Applications, Volume 390, Issue 12, 15 June 2011, Pages 2421--2428 · 6 pages
arxiv created 2010/10/09 · openalex publication_date 2011/02/26 · arxiv updated 2013/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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, et al., Phys. Rev. E 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, Discrete Math., 204 (1999) 203-229]. Our characterization of HVGs implies a linear time recognition algorithm. 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.