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A characterization of horizontal visibility graphs and combinatorics on words

Gutin, G; Mansour, T; Severini, S; (2011) A characterization of horizontal visibility graphs and combinatorics on words. PHYSICA A , 390 (12) 2421 - 2428. 10.1016/j.physa.2011.02.031.

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Abstract

A Horizontal Visibility Graph (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 Luque et al. [B. Luque, L. Lacasa, F. Ballesteros, J. Luque, Horizontal visibility graphs: exact results for random time series, Phys. Rev. E 80 (2009), 046103]. We prove that a graph is an HVG if and only if it is outerplanar and has a Hamilton path. Therefore, an HVG is a noncrossing graph, as defined in algebraic combinatorics Flajolet and Noy [P. Flajolet, M. Noy, Analytic combinatorics of noncrossing configurations, 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. (C) 2011 Elsevier B.V. All rights reserved.

Type:Article
Title:A characterization of horizontal visibility graphs and combinatorics on words
DOI:10.1016/j.physa.2011.02.031
Keywords:Networks, Time series, OUTERPLANAR GRAPHS, TIME
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Computer Science

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