Horizontal visibility graphs are uniquely determined by their directed degree sequence

2019 ◽  
Vol 536 ◽  
pp. 120923 ◽  
Author(s):  
Justin O’Pella
Keyword(s):  
Degree Sequence ◽  
Horizontal Visibility ◽  
Visibility Graphs

scholarly journals Analytic degree distributions of horizontal visibility graphs mapped from unrelated random series and multifractal binomial measures

2017 ◽  
Vol 119 (4) ◽  
pp. 48008 ◽  
Author(s):  
Wen-Jie Xie ◽  
Rui-Qi Han ◽  
Zhi-Qiang Jiang ◽  
Lijian Wei ◽  
Wei-Xing Zhou
Keyword(s):  
Random Series ◽  
Horizontal Visibility ◽  
Visibility Graphs

scholarly journals DETECTING SERIES PERIODICITY WITH HORIZONTAL VISIBILITY GRAPHS

2012 ◽  
Vol 22 (07) ◽  
pp. 1250160 ◽  
Author(s):  
ANGEL NUÑEZ ◽  
LUCAS LACASA ◽  
EUSEBIO VALERO ◽  
JOSE PATRICIO GÓMEZ ◽  
BARTOLO LUQUE
Keyword(s):  
Time Series ◽  
Graph Theory ◽  
Noise Reduction ◽  
Time Domain ◽  
Generic Properties ◽  
Horizontal Visibility ◽  
Visibility Graphs ◽  
Visibility Algorithm ◽  
In Series ◽  
Periodic Signals

The horizontal visibility algorithm was recently introduced as a mapping between time series and networks. The challenge lies in characterizing the structure of time series (and the processes that generated those series) using the powerful tools of graph theory. Recent works have shown that the visibility graphs inherit several degrees of correlations from their associated series, and therefore such graph theoretical characterization is in principle possible. However, both the mathematical grounding of this promising theory and its applications are in its infancy. Following this line, here we address the question of detecting hidden periodicity in series polluted with a certain amount of noise. We first put forward some generic properties of horizontal visibility graphs which allow us to define a (graph theoretical) noise reduction filter. Accordingly, we evaluate its performance for the task of calculating the period of noisy periodic signals, and compare our results with standard time domain (autocorrelation) methods. Finally, potentials, limitations and applications are discussed.

scholarly journals The North–South Asymmetry of Sunspot Relative Numbers Based on Complex Network Technique

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2228
Author(s):  
Hengyu Xu ◽  
Yu Fei ◽  
Chun Li ◽  
Jiajuan Liang ◽  
Xinan Tian ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Complex Network ◽  
Degree Sequence ◽  
Nonlinear Behavior ◽  
Original Data ◽  
Magnetic Activity ◽  
Sunspot Activity ◽  
Data Series ◽  
The North ◽  
Visibility Graphs

Solar magnetic activity exhibits a complex nonlinear behavior, but its dynamic process has not been fully understood. As the complex network technique can better capture the dynamics of nonlinear system, the visibility graphs (VG), the horizontal visibility graphs (HVG), and the limited penetrable visibility graphs (LPVG) are applied to implement the mapping of sunspot relative numbers in the northern and southern hemispheres. The results show that these three methods can capture important information of nonlinear dynamics existing in the long-term hemispheric sunspot activity. In the presentation of the results, the network degree sequence of the HVG method changes preferentially to the original data series as well as the VG and the LPVG, while both the VG and the LPVG slightly lag behind the original time series, which provides some new ideas for the nonlinear dynamics of the hemispheric asymmetry in the two hemispheres. Meanwhile, the use of statistical feature-skewness values and complex network visibility graphs can yield some complementary information for mutual verification.

scholarly journals Horizontal Visibility graphs generated by type-II intermittency

2013 ◽  
Vol 47 (3) ◽  
pp. 035102 ◽  
Author(s):  
Ángel M Núñez ◽  
Lucas Lacasa ◽  
Jose Patricio Gómez
Keyword(s):  
Type Ii ◽  
Horizontal Visibility ◽  
Visibility Graphs

scholarly journals Characterization of river flow fluctuations via horizontal visibility graphs

2016 ◽  
Vol 444 ◽  
pp. 1003-1011 ◽  
Author(s):  
A.C. Braga ◽  
L.G.A. Alves ◽  
L.S. Costa ◽  
A.A. Ribeiro ◽  
M.M.A. de Jesus ◽  
...  
Keyword(s):  
River Flow ◽  
Horizontal Visibility ◽  
Visibility Graphs ◽  
Flow Fluctuations
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