A Review of Visibility Graph Methods Research in Time Series Complex Network Analysis

LI Hai-lin; WANG Jie; ZHOU Wen-hao; CAI Yu; LIN Wei-bin

doi:10.12263/DZXB.20230082

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A Review of Visibility Graph Methods Research in Time Series Complex Network Analysis

SURVEYS AND REVIEWS | 更新时间：2025-12-08

- A Review of Visibility Graph Methods Research in Time Series Complex Network Analysis
- ACTA ELECTRONICA SINICA Vol. 51, Issue 9, Pages: 2598-2622(2023)
- 作者机构：
  
  1.华侨大学工商管理学院，福建泉州 362021
  2.泉州师范学院商学院，福建泉州 362021
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China(71771094);National Social Science Foundation of China(22FGLB035);Social Science Planning Project of Fujian Province(FJ2020B088)
- DOI：10.12263/DZXB.20230082
  CLC： TP391.9;
- Received：30 January 2023，
  
  Revised：2023-06-20，
  
  Published：25 September 2023
- 稿件说明：
移动端阅览
李海林,王杰,周文浩等.时间序列复杂网络分析中的可视图方法研究综述[J].电子学报,2023,51(09):2598-2622.

LI Hai-lin,WANG Jie,ZHOU Wen-hao,et al.A Review of Visibility Graph Methods Research in Time Series Complex Network Analysis[J].ACTA ELECTRONICA SINICA,2023,51(09):2598-2622.
李海林,王杰,周文浩等.时间序列复杂网络分析中的可视图方法研究综述[J].电子学报,2023,51(09):2598-2622. DOI： 10.12263/DZXB.20230082.

LI Hai-lin,WANG Jie,ZHOU Wen-hao,et al.A Review of Visibility Graph Methods Research in Time Series Complex Network Analysis[J].ACTA ELECTRONICA SINICA,2023,51(09):2598-2622. DOI： 10.12263/DZXB.20230082.

摘要

可视图是将时间序列转换成复杂网络的重要方法之一，也是连接非线性信号分析和复杂网络之间的全新视角，在经济金融、生物医学、工业工程等领域均应用广泛.可视图的拓扑结构继承了原始时间序列的重要性质，稳定且易于实现，通过可视图网络的相关统计特性，可区分特定时间序列数据下的特定行为.首先本文介绍了可视图方法在时间序列复杂网络分析中的相关研究，并通过必要性与可行性分析，充分说明可视图方法的优势所在.然后本文阐述了经典可视图和水平可视图方法的具体步骤及主要性质，从算法的过程改进、效率提升和可视图应用几个方面对现阶段可视图相关研究进行综述，介绍了众多可视图方法的基本过程，分析了可视图算法的识别抗噪能力和建网效率，并归纳整理了这些可视图方法的主要特性与适用范围.另外，本文复现了目前几种主流可视图算法，并公开相关的算法代码以供参考使用.通过对可视图相关研究的综述分析，可了解现阶段可视图的主要研究方向，为未来相关研究提供思路，并为时间序列复杂网络分析奠定基础.

Abstract

Visibility graph is one of the important methods for converting time series into complex networks

building a bridge between nonlinear signal analysis and complex networks with a new perspective

which is widely used in economic

biomedical

physics and other fields. Visibility graph inherits the dynamics of the original time series

is stable and easy to implement

and can distinguish specific behaviors under specific time series data by the relevant statistical properties of visibility graph. In this paper

we first introduce the application of the visibility graph in the analysis of time series complex networks. The advantages of the visibility graph are fully explained through the necessity and feasibility analysis. Then we describe the steps and main properties of basic visibility graph and horizontal visibility graph

and then review the current research on visibility graph from the following aspects: process improvement of algorithms

efficiency improvement of algorithms and visibility graph applications. We introduce the process of numerous visibility graph methods. We also summarize the main characteristics of these methods

analyze the recognition capability

anti-noise capability and network construction efficiency of visibility graph algorithms. In addition

we implement some algorithms and expose the codes for the general scholars to learn and use. Through the review and analysis of visibility graph related research

we can understand the main research directions of visibility graph at this stage

provide thinking for future related research

and establish the foundation for time series complex network analysis.

关键词

Keywords

references

李海林 , 邬先利 . 基于时间序列聚类的主题发现与演化分析研究 [J]. 情报学报 , 2019 , 38 ( 10 ): 1041 - 1050 .

LI H L , WU X L . Research on topic discovery and evolution based on time series clustering [J]. Journal of the China Society for Scientific and Technical Information , 2019 , 38 ( 10 ): 1041 - 1050 . (in Chinese)

李大社 , 孙元威 , 阮俊虎 . 基于GOSSA和HMM的时间序列预测算法 [J]. 电子学报 , DOI: 10.12263/DZXB. 20220856 http://dx.doi.org/10.12263/DZXB.20220856 .

LI D S , SUN Y W , RUAN J H . Time series prediction algorithm based on GOSSA and HMM [J]. Acta Electronica Sinica , DOI: 10.12263/DZXB.20220856. http://dx.doi.org/10.12263/DZXB.20220856. (in Chinese)

罗远兴 , 李志红 , 梁兴 , 等 . 基于EMD-LS的非平稳时间序列多重分形去趋势波动分析方法 [J]. 电子学报 , 2021 , 49 ( 12 ): 2323 - 2329 .

LUO Y X , LI Z H , LIANG X , et al . Multi-fractal detrended fluctuation analysis method for non-stationary time series based on EMD-LS [J]. Acta Electronica Sinica , 2021 , 49 ( 12 ): 2323 - 2329 . (in Chinese)

LI H L . Time works well: Dynamic time warping based on time weighting for time series data mining [J]. Information Sciences , 2021 , 547 : 592 - 608 .

WATTS D J , STROGATZ S H . Collective dynamics of ‘small-world’ networks [J]. Nature , 1998 , 393 : 440 - 442 .

BARABASI A L , ALBERT R . Emergence of scaling in random networks [J]. Science , 1999 , 286 : 509 - 512 .

ZHANG J , SMALL M . Complex network from pseudoperiodic time series: Topology versus dynamics [J]. Physical Review Letters , 2006 , 96 ( 23 ): 238701 .

LACASA L , LUQUE B , BALLESTEROS F , et al . From time series to complex networks: The visibility graph [J]. Proceedings of the National Academy of Sciences of the United States of America , 2008 , 105 ( 13 ): 4972 - 4975 .

LUQUE B , LACASA L , BALLESTEROS F , et al . Horizontal visibility graphs: Exact results for random time series [J]. Physical Review E , 2009 , 80 ( 4 ): 046103 .

BEZSUDNOV I V , SNARSKII A A . From the time series to the complex networks: The parametric natural visibility graph [J]. Physica A: Statistical Mechanics and Its Applications , 2014 , 414 : 53 - 60 .

周婷婷 , 金宁德 , 高忠科 , 等 . 基于有限穿越可视图的时间序列网络模型 [J]. 物理学报 , 2012 , 61 ( 3 ): 86 - 96 ..

ZHOU T T , JIN N D , GAO Z K , et al . Limited penetrable visibility graph for establishing complex network from time series [J]. Acta Physica Sinica , 2012 , 61 ( 3 ): 86 - 96 . (in Chinese)

GAO Z K , JIN N D , WANG W X , et al . Motif distributions in phase-space networks for characterizing experimental two-phase flow patterns with chaotic features [J]. Physical Review E , 2010 , 82 : 016210 .

XU X K , ZHANG J , SMALL M . Superfamily phenomena and motifs of networks induced from time series [J]. Proceedings of the National Academy of Sciences of the United States of America , 2008 , 105 ( 50 ): 19601 - 19605 .

MARWAN N , CARMEN ROMANO M , THIEL M , et al . Recurrence plots for the analysis of complex systems [J]. Physics Reports , 2007 , 438 ( 5/6 ): 237 - 329 .

MARWAN N , DONGES J F , ZOU Y , et al . Complex network approach for recurrence analysis of time series [J]. Physics Letters A , 2009 , 373 ( 46 ): 4246 - 4254 .

曾明 , 王二红 , 赵明愿 , 等 . 基于时间序列符号化模式表征的有向加权复杂网络 [J]. 物理学报 , 2017 , 66 ( 21 ): 210502 .

ZENG M , WANG E H , ZHAO M Y , et al . Directed weighted complex networks based on time series symbolic pattern representation [J]. Acta Physica Sinica , 2017 , 66 ( 21 ): 210502 . (in Chinese)

ZOU Y , DONNER R V , MARWAN N , et al . Complex network approaches to nonlinear time series analysis [J]. Physics Reports , 2019 , 787 : 1 - 97 .

LACASA L , LUQUE B , LUQUE J , et al . The visibility graph: A new method for estimating the Hurst exponent of fractional Brownian motion [J]. EPL (Europhysics Letters) , 2009 , 86 ( 3 ): 30001 .

LACASA L , TORAL R . Description of stochastic and chaotic series using visibility graphs [J]. Physical Review E , 2010 , 82 ( 3 ): 036120 .

LACASA L , NUÑEZ A , ROLDÁN É , et al . Time series irreversibility: A visibility graph approach [J]. The European Physical Journal B , 2012 , 85 ( 6 ): 217 .

NUÑEZ A , LACASA L , VALERO E , et al . Detecting series periodicity with horizontal visibility graphs [J]. International Journal of Bifurcation and Chaos , 2012 , 22 ( 7 ): 1250160 .

NÚÑEZ Á M , LUQUE B , LACASA L , et al . Horizontal visibility graphs generated by type-I intermittency [J]. Physical Review E , 2013 , 87 ( 5 ): 052801 .

NÚÑEZ Á M , LACASA L , GÓMEZ J P . Horizontal visibility graphs generated by type-II intermittency [J]. Journal of Physics A: Mathematical and Theoretical , 2014 , 47 ( 3 ): 035102 .

LUQUE B , BALLESTEROS F J , NÚÑEZ A M , et al . Quasiperiodic graphs: Structural design, scaling and entropic properties [J]. Journal of Nonlinear Science , 2013 , 23 ( 2 ): 335 - 342 .

LUQUE B , LACASA L , BALLESTEROS F J , et al . Feigenbaum graphs: A complex network perspective of chaos [J]. PLoS One , 2011 , 6 ( 9 ): e22411 .

LUQUE B , LACASA L , BALLESTEROS F J , et al . Analytical properties of horizontal visibility graphs in the Feigenbaum scenario [J]. Chaos , 2012 , 22 ( 1 ): 013109 .

LUQUE B , LACASA L , ROBLEDO A . Feigenbaum graphs at the onset of chaos [J]. Physics Letters A , 2012 , 376 ( 47/48 ): 3625 - 3629 .

FLANAGAN R , LACASA L , NICOSIA V . On the spectral properties of Feigenbaum graphs [J]. Journal of Physics A: Mathematical and Theoretical , 2020 , 53 ( 2 ): 025702 .

FLANAGAN R , LACASA L . Irreversibility of financial time series: A graph-theoretical approach [J]. Physics Letters A , 2016 , 380 ( 20 ): 1689 - 1697 .

SHAO Z G . Network analysis of human heartbeat dynamics [J]. Applied Physics Letters , 2010 , 96 ( 7 ): 073703 .

DONNER R V , DONGES J F . Visibility graph analysis of geophysical time series: Potentials and possible pitfalls [J]. Acta Geophysica , 2012 , 60 ( 3 ): 589 - 623 .

LACASA L , JUST W . Visibility graphs and symbolic dynamics [J]. Physica D: Nonlinear Phenomena , 2018 , 374/375 : 35 - 44 .

WANG N , LI D , WANG Q W . Visibility graph analysis on quarterly macroeconomic series of China based on complex network theory [J]. Physica A: Statistical Mechanics and Its Applications , 2012 , 391 ( 24 ): 6543 - 6555 .

GAO Y Y , YU D J . Total variation on horizontal visibility graph and its application to rolling bearing fault diagnosis [J]. Mechanism and Machine Theory , 2020 , 147 : 103768 .

ZHANG P T , NING P Y , CAO R H , et al . Analysis of climate change characteristics in Xi'an based on the visibility graph [J]. Frontiers in Physics , 2021 , 9 : 702064 .

SUPRIYA S , SIULY S , WANG H , et al . Weighted visibility graph with complex network features in the detection of epilepsy [J]. IEEE Access , 2016 , 4 : 6554 - 6566 .

ANGEL M , LACASA L , PATRICIO J , et al . Visibility algorithms: A short review [M]// New Frontiers in Graph Theory . Rijeka : InTech , 2012 : 119 - 152 .

汤胤 , 易娜 , 毛景慧 . 基于有向有限穿越可视图的时间序列伴生网络 [J]. 系统工程学报 , 2017 , 32 ( 2 ): 156 - 162, 264 .

TANG Y , YI N , MAO J H . Derived network based on directed limited penetrable visibility graph for time series [J]. Journal of Systems Engineering , 2017 , 32 ( 2 ): 156 - 162, 264 . (in Chinese)

XUAN Q , ZHOU J C , QIU K F , et al . CLPVG: Circular limited penetrable visibility graph as a new network model for time series [J]. Chaos , 2022 , 32 ( 1 ): 013130 .

WANG M G , VILELA A L M , DU R J , et al . Topological properties of the limited penetrable horizontal visibility graph family [J]. Physical Review. E , 2018 , 97 ( 5 ): 052117 .

GAO Z K , CAI Q , YANG Y X , et al . Time-dependent limited penetrable visibility graph analysis of nonstationary time series [J]. Physica A: Statistical Mechanics and Its Applications , 2017 , 476 : 43 - 48 .

LI X M , SUN M , GAO C X , et al . The parametric modified limited penetrable visibility graph for constructing complex networks from time series [J]. Physica A: Statistical Mechanics and Its Applications , 2018 , 492 : 1097 - 1106 .

REN W K , JIN N D . Sequential limited penetrable visibility-graph motifs [J]. Nonlinear Dynamics , 2020 , 99 ( 3 ): 2399 - 2408 .

AHMADLOU M , ADELI H , ADELI A . Improved visibility graph fractality with application for the diagnosis of autism spectrum disorder [J]. Physica A: Statistical Mechanics and Its Applications , 2012 , 391 ( 20 ): 4720 - 4726 .

BOSE R , SAMANTA K , MODAK S , et al . Augmenting neuromuscular disease detection using optimally parameterized weighted visibility graph [J]. IEEE Journal of Biomedical and Health Informatics , 2021 , 25 ( 3 ): 685 - 692 .

ZHU G H , LI Y , WEN P . Epileptic seizure detection in EEGs signals using a fast weighted horizontal visibility algorithm [J]. Computer Methods and Programs in Biomedicine , 2014 , 115 ( 2 ): 64 - 75 .

ZENG M , XU W K , ZHAO C Y , et al . Weighted complex network based on visibility angle measurement [C]// 2020 39th Chinese Control Conference (CCC) . Piscataway : IEEE , 2020 : 1138 - 1143 .

LI H L , LIU Z C . Multivariate time series clustering based on complex network [J]. Pattern Recognition , 2021 , 115 : 107919 .

LI H L , DU T . Multivariate time-series clustering based on component relationship networks [J]. Expert Systems With Applications , 2021 , 173 : 114649 .

LACASA L , NICOSIA V , LATORA V . Network structure of multivariate time series [J]. Scientific Reports , 2015 , 5 : 15508 .

GAO Z K , LIU M X , DANG W D , et al . Multilayer limited penetrable visibility graph for characterizing the gas-liquid flow behavior [J]. Chemical Engineering Journal , 2021 , 407 : 127229 .

CAI Q , GAO Z K , YANG Y X , et al . Multiplex limited penetrable horizontal visibility graph from EEG signals for driver fatigue detection [J]. International Journal of Neural Systems , 2019 , 29 ( 5 ): 1850057 .

GAO Z K , GUO W , CAI Q , et al . Characterization of SSMVEP-based EEG signals using multiplex limited penetrable horizontal visibility graph [J]. Chaos , 2019 , 29 ( 7 ): 073119 .

郭威 . 基于有限穿越可视图和深度学习的SSMVEP脑电信号分类及疲劳机制研究 [D]. 天津 : 天津大学 , 2019 .

GUO W . Limited Penetrable Visibility Graph and Deep Learning for SSMVEP EEG Signals Classification and Fatigue Mechanism Characterization [D]. Tianjin : Tianjin University , 2019 . (in Chinese)

REN W K , JIN N D . Vector visibility graph from multivariate time series: A new method for characterizing nonlinear dynamic behavior in two-phase flow [J]. Nonlinear Dynamics , 2019 , 97 ( 4 ): 2547 - 2556 .

LIU J , LI Q Q . Planar visibility graph network algorithm for two dimensional timeseries [C]// 2017 29th Chinese Control and Decision Conference (CCDC) . Piscataway : IEEE , 2017 : 1352 - 1357 .

BHADURI S , BHADURI A . Searching for supersymmetry at LHC using the complex-network-based method of the three-dimensional visibility-graph [J]. Physics , 2020 , 2 ( 3 ): 436 - 454 .

GAO Z K , CAI Q , YANG Y X , et al . Multiscale limited penetrable horizontal visibility graph for analyzing nonlinear time series [J]. Scientific Reports , 2016 , 6 : 35622 .

HAN J . Analysis of gas-water flow transition characteristics based on multiscale limited penetrable visibility graph [J]. Scientific Reports , 2020 , 10 : 7030 .

LI W D , ZHAO X J . Multiscale horizontal-visibility-graph correlation analysis of stock time series [J]. EPL (Europhysics Letters) , 2018 , 122 ( 4 ): 40007 .

LI W , WANG H , ZHUANG L H , et al . Weighted multi-scale limited penetrable visibility graph for exploring atrial fibrillation rhythm [J]. Signal Processing , 2021 , 189 : 108288 .

LAN X , MO H M , CHEN S Y , et al . Fast transformation from time series to visibility graphs [J]. Chaos , 2015 , 25 ( 8 ): 083105 .

FANO YELA D , THALMANN F , NICOSIA V , et al . Online visibility graphs: Encoding visibility in a binary search tree [J]. Physical Review Research , 2020 , 2 ( 2 ): 023069 .

GHOSH S , DUTTA A . An efficient non-recursive algorithm for transforming time series to visibility graph [J]. Physica A: Statistical Mechanics and Its Applications , 2019 , 514 : 189 - 202 .

STEPHEN C . A scalable linear-time algorithm for horizontal visibility graph construction over long sequences [C]// 2021 IEEE International Conference on Big Data (Big Data) . Piscataway : IEEE , 2022 : 40 - 50 .

兰鑫 . 时间序列的复杂网络转换策略研究 [D]. 重庆 : 西南大学 , 2015 .

LAN X . The Study of Transformation from Time Series to Complex Networks [D]. Chongqing : Southwest University , 2015 .

IACOVACCI J , LACASA L . Visibility graphs for image processing [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence , 2020 , 42 ( 4 ): 974 - 987 .

ZHU D X , SEMBA S , YANG H J . Matching intensity for image visibility graphs: A new method to extract image features [J]. IEEE Access , 2021 , 9 : 12611 - 12621 .

PEI L , LI Z , LIU J . Texture classification based on image (natural and horizontal) visibility graph constructing methods [J]. Chaos , 2021 , 31 ( 1 ): 013128 .

AHADPOUR S , SADRA Y . Randomness criteria in binary visibility graph and complex network perspective [J]. Information Sciences , 2012 , 197 : 161 - 176 .

AHADPOUR S , SADRA Y , ARASTEHFARD Z . Markov-binary visibility graph: A new method for analyzing complex systems [J]. Information Sciences , 2014 , 274 : 286 - 302 .

IACOVACCI J , LACASA L . Sequential visibility-graph motifs [J]. Physical Review. E , 2016 , 93 : 042309

CHEN S Y , HU Y , MAHADEVAN S , et al . A visibility graph averaging aggregation operator [J]. Physica A: Statistical Mechanics and Its Applications , 2014 , 403 : 1 - 12 .

JIANG W , WEI B Y , ZHAN J , et al . A visibility graph power averaging aggregation operator: A methodology based on network analysis [J]. Computers & Industrial Engineering , 2016 , 101 : 260 - 268 .

XU P H , ZHANG R , DENG Y . A novel visibility graph transformation of time series into weighted networks [J]. Chaos , Solitons & Fractals, 2018 , 117 : 201 - 208 .

LIU L H , HUANG J , WANG H M . Visibility graph power geometric aggregation operator and its application in water, energy and food efficiency evaluation [J]. International Journal of Environmental Research and Public Health , 2020 , 17 ( 11 ): 3891 .

JIANG W , WEI B Y , TANG Y C , et al . Ordered visibility graph average aggregation operator: An application in produced water management [J]. Chaos , 2017 , 27 ( 2 ): 023117 .

WANG H P , MO H M , SADIQ R , et al . Ordered visibility graph weighted averaging aggregation operator: A methodology based on network analysis [J]. Computers & Industrial Engineering , 2015 , 88 : 181 - 190 .

LI M Z , ZHANG Q , DENG Y . A new probability transformation based on the ordered visibility graph [J]. International Journal of Intelligent Systems , 2016 , 31 ( 1 ): 44 - 67 .

CHEN L Y , DENG Y , CHEONG K H . Probability transformation of mass function: A weighted network method based on the ordered visibility graph [J]. Engineering Applications of Artificial Intelligence , 2021 , 105 : 104438 .

SONG X J , XIAO F Y . Combining time-series evidence: A complex network model based on a visibility graph and belief entropy [J]. Applied Intelligence , 2022 , 52 ( 9 ): 10706 - 10715 .

LODS A , ANQUETIL É , MACÉ S . Fuzzy visibility graph for structural analysis of online handwritten mathematical expressions [C]// 2019 International Conference on Document Analysis and Recognition (ICDAR) . Piscataway : IEEE , 2020 : 641 - 646 .

HU Y T , XIAO F Y . Time-series forecasting based on fuzzy cognitive visibility graph and weighted multisubgraph similarity [J]. IEEE Transactions on Fuzzy Systems , 2023 , 31 ( 4 ): 1281 - 1293 .

CHOUDHARY G I , AZIZ W , KHAN I R , et al . Analysing the dynamics of interbeat interval time series using grouped horizontal visibility graph [J]. IEEE Access , 2019 , 7 : 9926 - 9934 .

LANDE D V , SNARSKII A A , YAGUNOVA E V , et al . The use of horizontal visibility graphs to identify the words that define the informational structure of a text [C]// 2013 12th Mexican International Conference on Artificial Intelligence . Piscataway : IEEE , 2014 : 209 - 215 .

ZHU G H , LI Y , WEN P . Analysis and classification of sleep stages based on difference visibility graphs from a single-channel EEG signal [J]. IEEE Journal of Biomedical and Health Informatics , 2014 , 18 ( 6 ): 1813 - 1821 .

HU Y T , XIAO F Y . A novel method for forecasting time series based on directed visibility graph and improved random walk [J]. Physica A: Statistical Mechanics and Its Applications , 2022 , 594 : 127029 .

GAO Z K , CAI Q , YANG Y X , et al . Visibility graph from adaptive optimal kernel time-frequency representation for classification of epileptiform EEG [J]. International Journal of Neural Systems , 2017 , 27 ( 4 ): 1750005 .

江泽涛 , 秦嘉奇 , 张少钦 . 参数池化卷积神经网络图像分类方法 [J]. 电子学报 , 2020 , 48 ( 9 ): 1729 - 1734 .

JIANG Z T , QIN J Q , ZHANG S Q . Parameterized pooling convolution neural network for image classification [J]. Acta Electronica Sinica , 2020 , 48 ( 9 ): 1729 - 1734 . (in Chinese)

徐先峰 , 张丽 , 郎彬 , 等 . 引入感知模型的改进孪生卷积神经网络实现人脸识别算法研究 [J]. 电子学报 , 2020 , 48 ( 4 ): 643 - 647 .

XU X F , ZHANG L , LANG B , et al . Research on inception module incorporated Siamese convolutional neural networks to realize face recognition [J]. Acta Electronica Sinica , 2020 , 48 ( 4 ): 643 - 647 . (in Chinese)

权宇 , 李志欣 , 张灿龙 , 等 . 融合深度扩张网络和轻量化网络的目标检测模型 [J]. 电子学报 , 2020 , 48 ( 2 ): 390 - 397 .

QUAN Y , LI Z X , ZHANG C L , et al . Fusing deep dilated convolutions network and light-weight network for object detection [J]. Acta Electronica Sinica , 2020 , 48 ( 2 ): 390 - 397 . (in Chinese)

CAI Q , AN J P , GAO Z K . A multiplex visibility graph motif-based convolutional neural network for characterizing sleep stages using EEG signals [J]. Brain Science Advances , 2020 , 6 ( 4 ): 355 - 363 .

CAI Q , GAO Z K , AN J P , et al . A graph-temporal fused dual-input convolutional neural network for detecting sleep stages from EEG signals [J]. IEEE Transactions on Circuits and Systems II: Express Briefs , 2021 , 68 ( 2 ): 777 - 781 .

GAO Z K , LIU M X , DANG W D , et al . A novel complex network-based deep learning method for characterizing gas-liquid two-phase flow [J]. Petroleum Science , 2021 , 18 ( 1 ): 259 - 268 .

ZHANG X H , LANDSNESS E C , CHEN W , et al . Automated sleep state classification of wide-field calcium imaging data via multiplex visibility graphs and deep learning [J]. Journal of Neuroscience Methods , 2022 , 366 : 109421 .

CAI Q , AN J P , LI H Y , et al . Cross-subject emotion recognition using visibility graph and genetic algorithm-based convolution neural network [J]. Chaos , 2022 , 32 ( 9 ): 093110 .

ZHAN T X , HE Y P , LI H W , et al . DVS: Deep visibility series and its application in construction cost index forecasting [EB/OL]. ( 2021-11-07 )[ 2023-01-30 ]. https://arxiv.org/abs/2111.04071 https://arxiv.org/abs/2111.04071 .

WANG J L , LIANG S , WANG Y , et al . A weighted overlook graph representation of EEG data for absence epilepsy detection [C]// 2020 IEEE International Conference on Data Mining (ICDM) . Piscataway : IEEE , 2021 : 581 - 590 .

FLORINDO J B , LEE Y S , JUN K , et al . VisGraphNet: A complex network interpretation of convolutional neural features [J]. Information Sciences , 2021 , 543 : 296 - 308 .

WANG W N , MOHSENI P , KILGORE K L , et al . Cuff-less blood pressure estimation from photoplethysmography via visibility graph and transfer learning [J]. IEEE Journal of Biomedical and Health Informatics , 2022 , 26 ( 5 ): 2075 - 2085 .

袁冠 , 邴睿 , 刘肖 , 等 . 基于时空图神经网络的手势识别 [J]. 电子学报 , 2022 , 50 ( 4 ): 921 - 931 .

YUAN G , BING R , LIU X , et al . Spatial-temporal graph neural network based hand gesture recognition [J]. Acta Electronica Sinica , 2022 , 50 ( 4 ): 921 - 931 . (in Chinese)

高留杰 , 赵文 , 张君福 , 等 . G2S: 基于语义块的知识图谱问答语义解析 [J]. 电子学报 , 2021 , 49 ( 6 ): 1132 - 1141 .

GAO L J , ZHAO W , ZHANG J F , et al . G2S: Semantic segment based semantic parsing for question answering over knowledge graph [J]. Acta Electronica Sinica , 2021 , 49 ( 6 ): 1132 - 1141 . (in Chinese)

车向北 , 康文倩 , 邓彬 , 等 . 一种基于图神经网络的SDN路由性能预测模型 [J]. 电子学报 , 2021 , 49 ( 3 ): 484 - 491 .

CHE X B , KANG W Q , DENG B , et al . A prediction model of SDN routing performance based on graph neural network [J]. Acta Electronica Sinica , 2021 , 49 ( 3 ): 484 - 491 . (in Chinese)

LI C Y , MO L F , YAN R Q . Rolling bearing fault diagnosis based on horizontal visibility graph and graph neural networks [C]// 2020 International Conference on Sensing , Measurement & Data Analytics in the Era of Artificial Intelligence (ICSMD) . Piscataway : IEEE , 2020 : 275 - 279 .

LI C Y , MO L F , YAN R Q . Fault diagnosis of rolling bearing based on WHVG and GCN [J]. IEEE Transactions on Instrumentation and Measurement , 2021 , 70 : 1 - 11 .

XUAN Q , ZHOU J C , QIU K F , et al . AvgNet: Adaptive visibility graph neural network and its application in modulation classification [J]. IEEE Transactions on Network Science and Engineering , 2022 , 9 ( 3 ): 1516 - 1526 .

XIU Y X , REN X Y , ZHANG T , et al . Time labeled visibility graph for privacy-preserved physiological time series classification [C]// 2022 7th International Conference on Cloud Computing and Big Data Analytics (ICCCBDA) . Piscataway : IEEE , 2022 : 280 - 284 .

ZENG J E , TANG J J . Modeling dynamic traffic flow as visibility graphs: A network-scale prediction framework for lane-level traffic flow based on LPR data [J]. IEEE Transactions on Intelligent Transportation Systems , 2023 : 24 ( 4 ): 4173 - 4188 .

WANG J L , LIANG S , HE D K , et al . A sequential graph convolutional network with frequency-domain complex network of EEG signals for epilepsy detection [C]// 2020 IEEE International Conference on Bioinformatics and Biomedicine (BIBM) . Piscataway : IEEE , 2021 : 785 - 792 .

WADHERA T , MAHMUD M . Computing hierarchical complexity of the brain from electroencephalogram signals: A graph convolutional network-based approach [C]// 2022 International Joint Conference on Neural Networks (IJCNN) . Piscataway : IEEE , 2022 : 1 - 6 .

CHEN S M , FENG C , HUANG Y , et al . Small target detection in X-band sea clutter using the visibility graph [J]. IEEE Transactions on Geoscience and Remote Sensing , 2022 , 60 : 1 - 11 .

XU A D , WU T , ZHANG Y N , et al . Graph-based time series edge anomaly detection in smart grid [C]// 2021 7th IEEE Intl Conference on Big Data Security on Cloud (BigDataSecurity), IEEE Intl Conference on High Performance and Smart Computing, (HPSC) and IEEE Intl Conference on Intelligent Data and Security (IDS) . Piscataway : IEEE , 2021 : 1 - 6 .

LI D R , LI Z Y , XIN H H . Proportional identification of residential air-conditioning loads based on graph theory [C]// 2021 IEEE/IAS Industrial and Commercial Power System Asia (I&CPS Asia) . Piscataway : IEEE , 2021 : 1624 - 1629 .

BIANCHI F M , LIVI L , ALIPPI C , et al . Multiplex visibility graphs to investigate recurrent neural network dynamics [J]. Scientific Reports , 2017 , 7 : 44037 .

ROY S S , CHATTERJEE S , ROY S , et al . Accurate detection of bearing faults using difference visibility graph and bi-directional long short-term memory network classifier [J]. IEEE Transactions on Industry Applications , 2022 , 58 ( 4 ): 4542 - 4551 .

BRISTONE M , PRASAD R , ABUBAKAR A ALI . CPPCNDL: Crude oil price prediction using complex network and deep learning algorithms [J]. Petroleum , 2020 , 6 ( 4 ): 353 - 361 .

PAL M , TIWARI Y , REDDY T V , et al . An integrative method for COVID-19 patients classification from chest X-ray using deep learning network with image visibility graph as feature extractor [EB/OL]. ( 2021-11-21 )[ 2023-01-30 ]. https://www.medrxiv.org/content/10.1101/2021.11.17.21266472v1 https://www.medrxiv.org/content/10.1101/2021.11.17.21266472v1 .

SAMANTA K , CHATTERJEE S , BOSE R . Cross-subject motor imagery tasks EEG signal classification employing multiplex weighted visibility graph and deep feature extraction [J]. IEEE Sensors Letters , 2020 , 4 ( 1 ): 1 - 4 .

ALTUNDOĞAN T G , KARAKÖSE M . Cracked wall image classification based on deep neural network using visibility graph features [C]// 2021 International Conference on Innovation and Intelligence for Informatics, Computing, and Technologies (3ICT) . Piscataway : IEEE , 2021 : 36 - 39 .

ALTUNDOGAN T G , KARAKÖSE M . EEG signal classification with deep neural networks using visibility graphs [C]// 2022 26th International Conference on Information Technology (IT) . Piscataway : IEEE , 2022 : 1 - 4 .

李海林 , 林春培 . 基于时间序列聚类的科研成果关键词分析方法 [J]. 科研管理 , 2022 , 43 ( 1 ): 176 - 183 .

LI H L , LIN C P . An analysis of keywords of research achievements based on time series clustering [J]. Science Research Management , 2022 , 43 ( 1 ): 176 - 183 . (in Chinese)

孙晨峰 , 吕卫民 , 戴洪德 , 等 . 一种基于TimeGAN和OCSVM的多元退化设备小子样数据增广方法 [J]. 电子学报 , 2022 , 50 ( 11 ): 2678 - 2687 .

SUN C F , LÜ W M , DAI H D , et al . A small sample data augmentation method for multivariate degradation equipment based on TimeGAN and OCSVM [J]. Acta Electronica Sinica , 2022 , 50 ( 11 ): 2678 - 2687 . (in Chinese)

LI H L , WU Y J , CHEN Y W . Time is money: Dynamic-model-based time series data-mining for correlation analysis of commodity sales [J]. Journal of Computational and Applied Mathematics , 2020 , 370 : 112659 .

尚文利 , 石贺 , 赵剑明 , 等 . 基于SAE-LSTM的工艺数据异常检测方法 [J]. 电子学报 , 2021 , 49 ( 8 ): 1561 - 1568 .

SHANG W L , SHI H , ZHAO J M , et al . An anomaly detection method of process data based on SAE-LSTM [J]. Acta Electronica Sinica , 2021 , 49 ( 8 ): 1561 - 1568 . (in Chinese)

PARTIDA A , CRIADO R , ROMANCE M . Visibility graph analysis of IOTA and IoTeX price series: An intentional risk-based strategy to use 5G for IoT [J]. Electronics , 2021 , 10 ( 18 ): 2282 .

LIU R Y , CHEN Y . Analysis of stock price motion asymmetry via visibility-graph algorithm [J]. Frontiers in Physics , 2020 , 8 : 539521 .

HUANG Y S , MAO X Y , DENG Y . Natural visibility encoding for time series and its application in stock trend prediction [J]. Knowledge-Based Systems , 2021 , 232 : 107478 .

LIU X B , YUAN X S , LIU C , et al . Analysis of stock price data: Determinition of the optimal sliding-window length [J]. Frontiers in Physics , 2021 , 9 : 741106 .

XIU Y X , WANG G Y , CHAN W K V . Crash diagnosis and price rebound prediction in NYSE composite index based on visibility graph and time-evolving stock correlation network [J]. Entropy , 2021 , 23 ( 12 ): 1612 .

QU Z Q , ZHANG Y J , LI F . Analyzing levels of concern about joint punishment for dishonesty using the visibility graph network [J]. Frontiers in Physics , 2021 , 9 : 746660 .

MODAK S , ROY S S , SAMANTA K , et al . Detection of focal EEG signals employing weighted visibility graph [C]// 2020 International Conference on Computer , Electrical & Communication Engineering (ICCECE) . Piscataway : IEEE , 2020 : 1 - 5 .

MOHAMMADPOORY Z , NASROLAHZADEH M , HADDADNIA J . Epileptic seizure detection in EEGs signals based on the weighted visibility graph entropy [J]. Seizure , 2017 , 50 : 202 - 208 .

NASROLAHZADEH M , MOHAMMADPOORY Z , HADDADNIA J . Analysis of heart rate signals during meditation using visibility graph complexity [J]. Cognitive Neurodynamics , 2019 , 13 ( 1 ): 45 - 52 .

BHADURI A , GHOSH D . Quantitative assessment of heart rate dynamics during meditation: An ECG based study with multi-fractality and visibility graph [J]. Frontiers in Physiology , 2016 , 7 : 44 .

LI X , YANG D , LIU X , et al . Bridging time series dynamics and complex network theory with application to electrocardiogram analysis [J]. IEEE Circuits and Systems Magazine , 2012 , 12 ( 4 ): 33 - 46 .

马志怡 , 杨小冬 , 何爱军 , 等 . 基于多路可视图的健康与心梗患者心电图信号复杂网络识别 [J]. 物理学报 , 2022 , 71 ( 5 ): 48 - 57 .

MA Z Y , YANG X D , HE A J , et al . Complex network recognition of electrocardiograph signals in health and myocardial infarction patients based on multiplex visibility graph [J]. Acta Physica Sinica , 2022 , 71 ( 5 ): 48 - 57 . (in Chinese)

KONG T J , SHAO J E , HU J Y , et al . EEG-based emotion recognition using an improved weighted horizontal visibility graph [J]. Sensors , 2021 , 21 ( 5 ): 1870 .

XIONG H , SHANG P J , HOU F Z , et al . Visibility graph analysis of temporal irreversibility in sleep electroencephalograms [J]. Nonlinear Dynamics , 2019 , 96 ( 1 ): 1 - 11 .

XU J S , WANG M T , ZHANG J P , et al . Network theory based EHG signal analysis and its application in preterm prediction [J]. IEEE Journal of Biomedical and Health Informatics , 2022 , 26 ( 7 ): 2876 - 2887 .

LEÓN C , CARRAULT G , PLADYS P , et al . Early detection of late onset sepsis in premature infants using visibility graph analysis of heart rate variability [J]. IEEE Journal of Biomedical and Health Informatics , 2021 , 25 ( 4 ): 1006 - 1017 .

ZHANG D D , LONG X , XU L , et al . Characterizing cardiorespiratory interaction in preterm infants across sleep states using visibility graph analysis [J]. Journal of Applied Physiology , 2021 , 130 ( 4 ): 1015 - 1024 .

VARLEY T F , SPORNS O . Network analysis of time series: Novel approaches to network neuroscience [J]. Frontiers in Neuroscience , 2021 , 15 : 787068 .

CAI Z P , CHENG H Y , XING Y T , et al . Autonomic nervous activity analysis based on visibility graph complex networks and skin sympathetic nerve activity [J]. Frontiers in Physiology , 2022 : 1001415 .

MOZAFFARILEGHA M , ADELI H . Visibility graph analysis of speech evoked auditory brainstem response in persistent developmental stuttering [J]. Neuroscience Letters , 2019 , 696 : 28 - 32 .

CHEN J Y , WANG Z , ZHENG H B , et al . DGFE-VG: Dynamic gene feature extraction via visibility graph [C]// Proceedings of the 3rd International Conference on Medical and Health Informatics . New York : ACM , 2019 : 119 - 124 .

ZHENG M Z , DOMANSKYI S , PIERMAROCCHI C , et al . Visibility graph based temporal community detection with applications in biological time series [J]. Scientific Reports , 2021 , 11 : 5623 .

NOWAK J , ENG R C , MATZ T , et al . A network-based framework for shape analysis enables accurate characterization of leaf epidermal cells [J]. Nature Communications , 2021 , 12 : 458 .

ZERVOU M A , DOUTSI E , PAVLIDIS P , et al . Structural classification of proteins based on the computationally efficient recurrence quantification analysis and horizontal visibility graphs [J]. Bioinformatics , 2021 , 37 ( 13 ): 1796 - 1804 .

JI C , HU Y P , WANG K , et al . Identifiable temporal feature selection via horizontal visibility graph towards smart medical applications [J]. Interdisciplinary Sciences: Computational Life Sciences , 2021 , 13 ( 4 ): 717 - 730 .

ROY S S , CHATTERJEE S . Partial discharge detection framework employing spectral analysis of horizontal visibility graph [J]. IEEE Sensors Journal , 2021 , 21 ( 4 ): 4819 - 4826 .

YELA D F , STOWELL D , SANDLER M . Spectral visibility graphs: Application to similarity of harmonic signals [C]// 2019 27th European Signal Processing Conference (EUSIPCO) . Piscataway : IEEE , 2019 : 1 - 5 .

MALI P , MUKHOPADHYAY A , MANNA S K , et al . Multifractal analysis of charged particle distributions using horizontal visibility graph and sandbox algorithm [J]. Modern Physics Letters A , 2017 , 32 ( 8 ): 1750024 .

PLOCOSTE T , CARMONA-CABEZAS R , JIMÉNEZ-HORNERO F J , et al . Multifractal characterisation of particulate matter (PM10) time series in the Caribbean Basin using visibility graphs [J]. Atmospheric Pollution Research , 2021 , 12 ( 1 ): 100 - 110 .

MOHEBIAN P , AVAL S B B , NOORI M , et al . Visible particle series search algorithm and its application in structural damage identification [J]. Sensors , 2022 , 22 ( 3 ): 1275 .

WU Z F , PAN X D , FAN K P , et al . Device-free orientation detection based on CSI and visibility graph [J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems , 2021 , 51 ( 7 ): 4433 - 4442 .

CHI K , SHEN J H , LI Y , et al . Multi-function radar signal sorting based on complex network [J]. IEEE Signal Processing Letters , 2021 , 28 : 91 - 95 .

LIU S T , LEI Z S , GE Y , et al . Automatic radar antenna scan type recognition based onlimited penetrable visibility graph [J]. Journal of Systems Engineering and Electronics , 2021 , 32 ( 2 ): 437 - 446 .

WAN T , JIANG K L , LIAO J Y , et al . Research on LPI radar signal detection and parameter estimation technology [J]. Journal of Systems Engineering and Electronics , 2021 , 32 ( 3 ): 566 - 572 .

MIRALLES R , LARA G , CARRIÓN A , et al . Assessment of arrow-of-time metrics for the characterization of underwater explosions [J]. Sensors , 2021 , 21 ( 17 ): 5952 .

ACOSTA-TRIPAILAO B , MAX-MOERBECK W , PASTÉN D , et al . Assigning degrees of stochasticity to blazar light curves in the radio band using complex networks [EB/OL]. ( 2022-05-09 )[ 2023-01-30 ]. https://arxiv.org/abs/2205.04568 https://arxiv.org/abs/2205.04568 .

MUÑOZ V , GARCÉS N E . Analysis of pulsating variable stars using the visibility graph algorithm [J]. PLoS One , 2021 , 16 ( 11 ): e0259735 .

IACOBELLO G , SCARSOGLIO S , RIDOLFI L . Visibility graph analysis of wall turbulence time-series [J]. Physics Letters A , 2018 , 382 ( 1 ): 1 - 11 .

TAO X T , WU H X . Modified horizontal visibility graph and its application in turbulence [C]// Proceedings of the AIAA Scitech 2019 Forum . Reston : AIAA , 2019 : AIAA2019-1868.

CHOWDHURI S , IACOBELLO G , BANERJEE T . Visibility network analysis of large-scale intermittency in convective surface layer turbulence [J]. Journal of Fluid Mechanics , 2021 , 925 : A38 .

IACOBELLO G , RIDOLFI L , SCARSOGLIO S . Large-to-small scale frequency modulation analysis in wall-bounded turbulence via visibility networks [J]. Journal of Fluid Mechanics , 2021 , 918 : A13 .

IACOBELLO G , RIDOLFI L , SCARSOGLIO S . A review on turbulent and vortical flow analyses via complex networks [J]. Physica A: Statistical Mechanics and Its Applications , 2021 , 563 : 125476 .

JOHN R , JOHN M . Adaptation of the visibility graph algorithm for detecting time lag between rainfall and water level fluctuations in Lake Okeechobee [J]. Advances in Water Resources , 2019 , 134 : 103429 .

PIERINI J O , LOVALLO M , TELESCA L . Visibility graph analysis of wind speed records measured in central Argentina [J]. Physica A: Statistical Mechanics and Its Applications , 2012 , 391 ( 20 ): 5041 - 5048 .

TELESCA L , LOVALLO M . Analysis of seismic sequences by using the method of visibility graph [J]. EPL (Europhysics Letters) , 2012 , 97 ( 5 ): 50002 .

TELESCA L , LOVALLO M , AGGARWAL S K , et al . Precursory signatures in the visibility graph analysis of seismicity: An application to the Kachchh (Western India) seismicity [J]. Physics and Chemistry of the Earth , Parts A/B/C, 2015 , 85/86 : 195 - 200 .

TELESCA L , LOVALLO M , RAMIREZ-ROJAS A , et al . Investigating the time dynamics of seismicity by using the visibility graph approach: Application to seismicity of Mexican subduction zone [J]. Physica A: Statistical Mechanics and Its Applications , 2013 , 392 ( 24 ): 6571 - 6577 .

RAMÍREZ-ROJAS A , FLORES-MÁRQUEZ E L . Nonlinear statistical features of the seismicity in the subduction zone of tehuantepec isthmus, southern méxico [J]. Entropy , 2022 , 24 ( 4 ): 480 .

KUNDU S , OPRIS A , YUKUTAKE Y , et al . Extracting correlations in earthquake time series using visibility graph analysis [J]. Frontiers in Physics , 2021 , 9 : 656310 .

TELESCA L , THAI A T , LOVALLO M , et al . Visibility graph analysis of reservoir-triggered seismicity: The case of song tranh 2 hydropower, Vietnam [J]. Entropy , 2022 , 24 ( 11 ): 1620 .

TELESCA L , LOVALLO M , PIERINI J O . Visibility graph approach to the analysis of ocean tidal records [J]. Chaos , Solitons & Fractals, 2012 , 45 ( 9/10 ): 1086 - 1091 .

MARWAN N , DONGES J F , DONNER R V , et al . Nonlinear time series analysis of palaeoclimate proxy records [J]. Quaternary Science Reviews , 2021 , 274 : 107245 .

HU J , CHEN J H , ZHU P C , et al . Difference and cluster analysis on the carbon dioxide emissions in China during COVID-19 lockdown via a complex network model [J]. Frontiers in Psychology , 2022 , 12 : 795142 .

HU Y X , CHU C B , WU P , et al . A linear time series analysis of carbon price via a complex network approach [J]. Frontiers in Physics , 2022 , 10 : 1029600 .

GÓMEZ-GÓMEZ J , CARMONA-CABEZAS R , SÁNCHEZ- LÓPEZ E , et al . Analysis of air mean temperature anomalies by using horizontal visibility graphs [J]. Entropy , 2021 , 23 ( 2 ): 207 .

YIN Y , WANG W J , LI Q A , et al . Jensen-shannon divergence based on horizontal visibility graph for complex time series [J]. Fluctuation and Noise Letters , 2021 , 20 ( 2 ): 2150013 .

JOHN M , FERBINTEANU J . Detecting time lag between a pair of time series using visibility graph algorithm [J]. Communications in Statistics: Case Studies, Data Analysis and Applications , 2021 , 7 ( 3 ): 315 - 343 .

CHEN Y Y , WANG J , DENG B . Improve the estimation of Hurst exponents from visibility graph [C]// 2016 Chinese Control and Decision Conference (CCDC) . Piscataway : IEEE , 2016 : 2350 - 2353 .

KAKI B , FARHANG N , SAFARI H . Evidence of self-organized criticality in time series by the horizontal visibility graph approach [J]. Scientific Reports , 2022 , 12 : 16835 .

WANG H , SUN Y S . A community evolution model based on visibility graph [C]// 2015 34th Chinese Control Conference (CCC) . Piscataway : IEEE , 2015 : 2045 - 2049 .

LIU J , LIU H L , HUANG Z J , et al . Differ multivariate timeseries from each other based on a simple multiplex visibility graphs technique [C]// 2015 Sixth International Conference on Intelligent Control and Information Processing (ICICIP) . Piscataway : IEEE , 2016 : 289 - 295 .

CAMPANHARO A S L O , SIRER M I , MALMGREN R D , et al . Duality between time series and networks [J]. PLoS One , 2011 , 6 ( 8 ): e23378 .

LI Q , CHEN Y G , AO N , et al . Echo state network-based visibility graph method for nonlinear time series prediction [C]// 2018 Chinese Control and Decision Conference (CCDC) . Piscataway : IEEE , 2018 : 1854 - 1859 .

DE SOUZA MOREIRA F R , VERRI F A N , YONEYAMA T . Maximum visibility: A novel approach for time series forecasting based on complex network theory [J]. IEEE Access , 2022 , 10 : 8960 - 8973 .

HU Y T , XIAO F Y . Network self attention for forecasting time series [J]. Applied Soft Computing , 2022 , 124 : 109092 .

WEN T , CHEN H L , CHEONG K H . Visibility graph for time series prediction and image classification: A review [J]. Nonlinear Dynamics , 2022 , 110 ( 4 ): 2979 - 2999 .

FLORINDO J , MARTINEZ BRUNO O . Using fractal interpolation over complex network modeling of deep texture representation [C]// 2022 Eleventh International Conference on Image Processing Theory, Tools and Applications (IPTA) . Piscataway : IEEE , 2022 : 1 - 5 .

LI H , LIAO J W , LIU X Y . Merging and prioritizing optimization in block I/O scheduling of disk storage [J]. Journal of Circuits, Systems and Computers , 2021 , 30 ( 10 ): 2150186 .

STEPHEN M , GU C G , YANG H J . Visibility graph based time series analysis [J]. PLoS One , 2015 , 10 ( 11 ): e0143015 .

LI H L , WANG J , CAI Y , et al . Visibility-Graph [EB/OL]. ( 2022-05-15 )[ 2023-01-30 ]. https://github.com/DENG- GONG/Visibility-Graph https://github.com/DENG-GONG/Visibility-Graph .

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