کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
978195 | 933259 | 2011 | 8 صفحه PDF | دانلود رایگان |

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.
► We prove that a graph is an HVG if and only if it is outerplanar and has a Hamilton path. This an exact characterization of HVGs.
► Based on the characterization, we point out that if we are given a graph, we have an efficient algorithm to determine if there is a time series associated to the graph.
► We open a new direction to study HVGs via algebraic combinatorics on words, a well-established area of research.
Journal: Physica A: Statistical Mechanics and its Applications - Volume 390, Issue 12, 15 June 2011, Pages 2421–2428