The DOI matches its Crossref record; 22 of the 22 references it cites were found in a registry or an index; none of the 9 sources its claims cite is checked for support yet.
From time series to complex networks: the visibility graph
Open accessAbstract
In this work we present a simple and fast computational method, the visibility algorithm , that converts a time series into a graph. The constructed graph inherits several properties of the series in its structure. Thereby, periodic series convert into regular graphs, and random series do so into random graphs. Moreover, fractal series convert into scale-free networks, enhancing the fact that power law degree distributions are related to fractality, something highly discussed recently. Some remarkable examples and analytical tools are outlined to test the method's reliability. Many different measures, recently developed in the complex network theory, could by means of this new approach characterize time series from a new point of view.
Overview
AI snapshot
Written from the paper’s full text.
TL;DR
The paper introduces the visibility algorithm, which maps a time series into a graph by connecting data points that can “see” each other without intermediate heights blocking the line of sight. It shows that periodic series yield regular graphs, random series yield random graphs with exponential degree tails, and fractal series yield scale-free visibility graphs.
Key findings
- Periodic time series map to regular graphs whose discrete degree distribution has peaks related to the series period; the example in Fig. 1 is a period-4 series.
- A random series of \(10^6\) data from \(U[0,1]\) produces a visibility graph whose degree distribution has an exponential tail, attributed to rare large values acting as hubs.
- Brownian motion visibility graphs are scale-free with \(P(k) \sim k^{-\alpha}\), \(\alpha = 2.00 \pm 0.01\), and show a Small-World effect with \(L(N) = 1.21 + 0.51\log(N)\).
- Conway series visibility graphs are scale-free with \(\alpha = 1.2 \pm 0.1\) and scale-invariant path length \(L(N) = 0.76 N^{0.38}\); a deterministic fractal example is also shown analytically to yield a power-law degree distribution.
Methods
- The visibility algorithm maps each time-series datum to a node and links two nodes if the straight line between their data values does not intersect any intermediate data height.
- The paper analyzes periodic series, a random series of \(10^6\) points from \(U[0,1]\), Brownian motion of \(10^6\) data, a Conway series of \(4 \cdot 10^6\) data, and a deterministic iterated fractal series.
- Main analyses include degree distributions \(P(k)\), mean path length \(L(N)\), and analytical recurrence relations for the deterministic fractal example.
Limitations
- The paper states that information is inevitably lost because the network structure is completely determined by the binary adjacency matrix; for example, periodic series \(T_1 = \{\ldots,3,1,3,1,\ldots\}\) and \(T_2 = \{\ldots,3,2,3,2,\ldots\}\) have the same visibility graph despite being quantitatively different.
- The paper states that it only tackles undirected graphs, while a directed version related to temporal axis direction is left for further work.
- The paper notes that the simple deterministic fractal example does not provide a general explanation of why fractality translates into power-law distributions, though it may stand as a generic way to deal with deterministic fractal series generated by iteration.
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Claims the paper makes
14 Own interpretation · 7 No basis given · 6 Own result · 4 Sources not found · 1 No full text of the sources · 1 Not checked yet · 1 Own method
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The degree distribution of this graph is formed by a finite number of peaks related to the series period, much in the vein of the Fourier Power Spectrum of a time series.”
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In the paper
“( iii ) invariant under affine transformations of the series data: the visibility criterium is invariant under rescaling of both horizontal and vertical axis, as well as under horizontal and vertical translations (see figure 2).”
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In the paper
“The tail of this distribution fits quite well an exponential distribution, as expected.”
- Also stated in: § Resumen · p. 3 · plain
“random series convert into exponential random graphs”
boostedcorrelational- Asserted: passes — The authors put it forward as true.
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- Also stated in: § Resumen · p. 3 · plain
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In this letter we introduce a new tool in time series analysis: the visibility graph . This algorithm maps a time series into a network.”
- Also stated in: § Resumen · p. 1 · plain
“the visibility algorithm , that converts a time series into a graph.”
plaindirect- Asserted: passes — The authors put it forward as true.
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- Also stated in: § Resumen · p. 1 · plain
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In the paper
“( ii ) undirected: the way the algorithm is built up, there is no direction defined in the links.”
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In the paper
“( i ) connected: each node sees at least its nearest neighbors (left and right).”
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In the paper
“This one is a power law P ( k ) ∼ k -α with α = 1 , 2 ± 0 , 1.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“that is, the degree distribution related to the C-nodes is a power law.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“This one is a power law P ( k ) ∼ k -α with α = 2 , 00 ± 0 , 01.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“It is indeed due to these 'unlikely' large values (the hubs) that the tail of the degree distribution deviates from the Poisson distribution.”
plaindirect- Asserted: passes — The authors put it forward as true.
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- It may state two separate claims as one. 6
- Probably not a substantial claim. 3
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“while the Brownian visibility graph seems to evidence the SmallWorld effect (right top figure 4) as L ( N ) ∼ log( N )”
- Also stated in: § Referencias · p. 12 · plain
“The best fitting provides a logarithmic scaling L ( N ) = 1 , 21 + 0 , 51log( N ). This network shows Small-World effect in addition to be scale-free.”
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It may state two separate claims as one.
- Also stated in: § Referencias · p. 12 · plain
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“the Conway series shows in turn a self-similar relation (right bottom figure 4) of the shape L ( N ) ∼ N β”
- Also stated in: § Referencias · p. 12 · plain
“The best fitting provides a power law scaling L ( N ) = 0 , 76 N 0 , 38 . Then, this network is scale-invariant.”
plaincorrelationalSingle case- Asserted: passes — The authors put it forward as true.
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- Also stated in: § Referencias · p. 12 · plain
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“nodes A and B have typically the same degree.”
- Also stated in: § Resumen · p. 4 · plain
“The degree of A and B is the same as the right degree of C”
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- Also stated in: § Resumen · p. 4 · plain
In the paper
“Note that this summation agrees with the number of irreducible polynomials of degree at most n over the Galois field GF(2) [20]”
What the sources say
- Not checked — no full text of the sourcecites [20] K.H. Hicks, G.L. Mullen, and I. Sato, Distribution of irreducible polynomials over F 2 , in Finite Fields with Applications to Coding Theory, Cryptography and Related Areas (Oaxaca, 2001), 177-186, Springer, Berlin, 2002. source
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None of the sources cited for this claim have been checked yet.
In the paper
“some other fractal series have been also studied (Q series [16], Stern series [17], Thue-Morse series [18], etc) with similar results.”
What the sources say
- Not checked — no full text of the sourcecites [16] D. Hofstadter, G¨ odel, Escher, Bach , New York: Vintage Books, pp. 137-138 (1980).
- Not matchedcites [17] M.A. Stern, J. Reine Angew. Math. , 55, pp. 193-220 (1858).
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [18] M.R. Schroeder, Fractals, Chaos, and Power Laws , New York: W. H. Freeman (1991).
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaincorrelational- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“the method captures the hub repulsion phenomenon associated to fractal networks [8] and thus distinguishes scale free visibility graphs evidencing Small-World effect from those showing scale invariance.”
What the sources say
- Not matchedcites [8] C. Song, S. Havlin, H.A. Makse, Nat. Phys. 2 ,275 (2006).
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaindirect- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The structure of the time series is conserved in the graph topology: periodic series convert into regular graphs, random series into random graphs and fractal series into scale-free graphs.”
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“we may argue that the visibility graph can actually distinguish different types of fractality”
hedgedcorrelational- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
In the paper
“In every case the algorithm captures the random nature of the series, and the particular shape of the degree distribution of the visibility graph is related to the particular random process [4].”
What the sources say
- Not matchedcites [4]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plaincorrelational- Asserted: passes — The authors put it forward as true.
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Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“The resulting visibility graph has characteristics that reflect the equivalent time series temporal structure and can be used to identify trends.”
From PyIOmica: longitudinal omics analysis and trend identification (2020) · cites this paper as Lacasa et al., 2008
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Recent work on characterizing complex events focuses on using network/graph methodology that can capture non-linear behavior (Lacasa et al., 2008).”
From PyIOmica: longitudinal omics analysis and trend identification (2020) · cites this paper as Lacasa et al., 2008
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“The challenges in capturing relationships and dependencies among emotions indicate the necessity for an architecture that is both easy to construct and preserves the structure of the underlying signal in its topology to improve both performance and interpretability [21], [22].”
From Emotion Classification With Visibility Graphs (2025) · cites this paper as [22]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“In VVG, edge directionality stems from the projection-based asymmetry between multidimensional vectors.When M = 1, vectors reduce to scalars, eliminating projections and making visibility symmetric, resulting in an undirected graph [22], [25].”
From Emotion Classification With Visibility Graphs (2025) · cites this paper as [22]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“Time series are transformed into networks that conserve their topology, and allow the identification of varying temporal structures.”
From PyIOmica: longitudinal omics analysis and trend identification (2020) · cites this paper as Lacasa et al., 2008
The cited source says what the claim attributes to it.
In the citing paper
“To this end, visibility graphs offer an effective means of representing sequential signals by connecting data points according to their value-based visibility, thereby preserving the underlying temporal structure while introducing geometric relationships [22], [23].”
From Emotion Classification With Visibility Graphs (2025) · cites this paper as [22]
The cited source says what the claim attributes to it.
In the citing paper
“The vector visibility graph (VVG) algorithm [25] extends the univariate visibility graph [22], [24] concept to multivariate time series data”
From Emotion Classification With Visibility Graphs (2025) · cites this paper as [22]
The cited source says what the claim attributes to it.
In the citing paper
“This simple yet versatile transformation supports both scalar [22], [24] and vector representations [25], with applications spanning time series analysis and language processing [26], [27].”
From Emotion Classification With Visibility Graphs (2025) · cites this paper as [22]
The cited source says what the claim attributes to it.
In the citing paper
“The natural visibility graph (NVG) algorithm [22] is a foundational method for mapping univariate (scalar) time series into graph networks.”
From Emotion Classification With Visibility Graphs (2025) · cites this paper as [22]
Citations
Cites
Collective dynamics of ‘small-world’ networks
Watts, D. J., & Strogatz, S. H. (1998) · Nature · doi:10.1038/30918 · Cited by 43,060
Emergence of Scaling in Random Networks
Barabási, A.-L., & Albert, R. (1999) · Science · doi:10.1126/science.286.5439.509 · Cited by 36,135
An introduction to probability theory and its applications
(1958) · Journal of the Franklin Institute · doi:10.1016/0016-0032(58)90688-4 · Cited by 29,621
Statistical mechanics of complex networks
Albert, R., & Barabási, A.-L. (2002) · Reviews of Modern Physics · doi:10.1103/revmodphys.74.47 · Cited by 20,471
The Structure and Function of Complex Networks
Newman, M. E. J. (2003) · SIAM Review · doi:10.1137/s003614450342480 · Cited by 18,719
Complex networks: structure and dynamics
BOCCALETTI, S., LATORA, V, MORENO, Y., CHAVEZ, M., & HWANG, D. (2006) · Physics Reports · doi:10.1016/j.physrep.2005.10.009 · Cited by 11,010
An Introduction to Probability Theory and its Applications.
Kingmán, J. F. C., & Feller, W. (1972) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2344620 · Cited by 5,297
Bollobás, B. (1998) · Graduate texts in mathematics · doi:10.1007/978-1-4612-0619-4 · Cited by 3,867
An Introduction to Probability Theory.
Fristedt, B. E., & Moran, P. A. P. (1986) · Journal of the American Statistical Association · doi:10.2307/2288022 · Cited by 3,358
Dorogovtsev, S. N., & Mendes, J. F. F. (2002) · Advances In Physics · doi:10.1080/00018730110112519 · Cited by 3,219
Research works printed but not linked: 2
- J Conway Some Crazy Sequences, 1988).
- MA Stern J Reine Angew Math 55, 193–220 (1858).
Cited by
Sorted by citations
A survey of methods for time series change point detection
Aminikhanghahi, S., & Cook, D. J. (2016) · Knowledge and Information Systems · doi:10.1007/s10115-016-0987-z · Cited by 1,246
Horizontal visibility graphs: Exact results for random time series
Luque, B., Lacasa, L., Ballesteros, F., & Luque, J. (2009) · Physical Review E · doi:10.1103/physreve.80.046103 · Cited by 789
Self-citationComplex network approaches to nonlinear time series analysis
Zou, Y., Donner, R. V., Marwan, N., Donges, J. F., & Kurths, J. (2018) · Physics Reports · doi:10.1016/j.physrep.2018.10.005 · Cited by 636
Recurrence networks—a novel paradigm for nonlinear time series analysis
Donner, R. V., Zou, Y., Donges, J. F., Marwan, N., & Kurths, J. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/3/033025 · Cited by 618
Complex network approach for recurrence analysis of time series
Marwan, N., Donges, J. F., Zou, Y., et al. (2009) · Physics Letters A · doi:10.1016/j.physleta.2009.09.042 · Cited by 594
Superfamily phenomena and motifs of networks induced from time series
Xu, X.-K., Zhang, J., & SMALL, M. P. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0806082105 · Cited by 478
Multifractal analysis of financial markets: a review
Zhi-qiang Jiang, A., Xie, W.-J., Zhou, W., & Sornette, D. (2019) · Reports on Progress in Physics · doi:10.1088/1361-6633/ab42fb · Cited by 435
Recurrence based time series analysis by means of complex network methods
DONNER, R. V., SMALL, M., DONGES, J. F., MARWAN, N., ZOU, Y., XIANG, R., & KURTHS, J. (2011) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127411029021 · Cited by 423
The visibility graph: A new method for estimating the Hurst exponent of fractional Brownian motion
Lacasa, L., Luque, B., Luque, J., & Nuño, J. C. (2009) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/86/30001 · Cited by 395
Self-citationZhu, G., Li, Y., & Wen, P. P. (2014) · IEEE Journal of Biomedical and Health Informatics · doi:10.1109/jbhi.2014.2303991 · Cited by 381
Latora, V., Nicosia, V., & Russo, G. (2017) · Cambridge University Press eBooks · doi:10.1017/9781316216002 · Cited by 377
Approaching complexity by stochastic methods: From biological systems to turbulence
Friedrich, R., Peinke, J., Sahimi, M., & Tabar, M. R. R. (2011) · Physics Reports · doi:10.1016/j.physrep.2011.05.003 · Cited by 350
Sensitivity and Nonlinearity of Thermoacoustic Oscillations
Juniper, M. P., & Sujith, R. I. (2017) · Annual Review of Fluid Mechanics · doi:10.1146/annurev-fluid-122316-045125 · Cited by 344
Bianconi, G. (2018) · doi:10.1093/oso/9780198753919.001.0001 · Cited by 526
New diagnostic EEG markers of the Alzheimer’s disease using visibility graph
Ahmadlou, M., Adeli, H., & Adeli, A. (2010) · Journal of Neural Transmission · doi:10.1007/s00702-010-0450-3 · Cited by 319
Complex network analysis of time series
Gao, Z., SMALL, M. P., & Kurths, J. (2016) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/116/50001 · Cited by 302
Duality between Time Series and Networks
Campanharo, A. S. L. O., Sirer, M. I., Malmgren, R. D., Ramos, F. M., & Amaral, L. A. N. (2011) · PLoS ONE · doi:10.1371/journal.pone.0023378 · Cited by 270
Network structure of multivariate time series
Lacasa, L., Nicosia, V., & Latora, V. (2015) · Scientific Reports · doi:10.1038/srep15508 · Cited by 252
Self-citationDescription of stochastic and chaotic series using visibility graphs
Lacasa, L., & Toral, R. (2010) · Physical Review E · doi:10.1103/physreve.82.036120 · Cited by 251
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Gao, Z., Dang, W., Wang, X., Hong, X., Hou, L., Ma, K., & Perc, M. (2020) · Cognitive Neurodynamics · doi:10.1007/s11571-020-09626-1 · Cited by 232
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Supriya, S., Siuly, S., Wang, H., Cao, J., & Zhang, Y. (2016) · IEEE Access · doi:10.1109/access.2016.2612242 · Cited by 216
Network analysis of particles and grains
Papadopoulos, L., Porter, M. A., Daniels, K. E., & Bassett, D. S. (2018) · Journal of Complex Networks · doi:10.1093/comnet/cny005 · Cited by 216
A Survey of Topological Machine Learning Methods
Hensel, F., Moor, M., & Rieck, B. (2021) · Frontiers in Artificial Intelligence · doi:10.3389/frai.2021.681108 · Cited by 209
Complex network from time series based on phase space reconstruction
Gao, Z., & Jin, N. (2009) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.3227736 · Cited by 203
A systematic review on recent advances in autonomous mobile robot navigation
Loganathan, A., & Ahmad, N. S. (2023) · Engineering Science and Technology an International Journal · doi:10.1016/j.jestch.2023.101343 · Cited by 220
Multiscale limited penetrable horizontal visibility graph for analyzing nonlinear time series
Gao, Z., Cai, Q., Yang, Y., Dang, W., & Zhang, S. (2016) · Scientific Reports · doi:10.1038/srep35622 · Cited by 187
Graph Theory and Brain Connectivity in Alzheimer’s Disease
del'Etoile, J., & Adeli, H. (2017) · The Neuroscientist · doi:10.1177/1073858417702621 · Cited by 188
Gao, Z., Fang, P., Ding, M.-S., & Jin, N. (2014) · Experimental Thermal and Fluid Science · doi:10.1016/j.expthermflusci.2014.09.008 · Cited by 186
Improved visibility graph fractality with application for the diagnosis of Autism Spectrum Disorder
Ahmadlou, M., Adeli, H., & Adeli, A. (2012) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2012.04.025 · Cited by 180
Gao, Z., Cai, Q., Yang, Y., et al. (2016) · International Journal of Neural Systems · doi:10.1142/s0129065717500058 · Cited by 175
Sleep stage classification with ECG and respiratory effort
Fonseca, P. M., Long, X., Radha, M., Haakma, R., Aarts, R. M., & Rolink, J. (2015) · Physiological Measurement · doi:10.1088/0967-3334/36/10/2027 · Cited by 168
Epileptic seizure detection in EEGs signals using a fast weighted horizontal visibility algorithm
Zhu, G., Li, Y., & Wen, P. P. (2014) · Computer Methods and Programs in Biomedicine · doi:10.1016/j.cmpb.2014.04.001 · Cited by 166
Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems
McCullough, M., SMALL, M. P., Stemler, T., et al. (2015) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4919075 · Cited by 160
Li, R., Yuan, X., Radfar, M., Marendy, P., Ni, W., O'Brien, T. J., & Casillas-Espinosa, P. M. (2021) · IEEE Reviews in Biomedical Engineering · doi:10.1109/rbme.2021.3122522 · Cited by 166
Visibility graph similarity: A new measure of generalized synchronization in coupled dynamic systems
Ahmadlou, M., & Adeli, H. (2011) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2011.09.008 · Cited by 157
Visibility network of United States hurricanes
Elsner, J. B., Jagger, T. H., & Fogarty, E. A. (2009) · Geophysical Research Letters · doi:10.1029/2009gl039129 · Cited by 152
Liu, C., Zhou, W., & Yuan, W. (2010) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2010.02.043 · Cited by 151
Sujith, R. I., & Unni, V. R. (2020) · Physics of Fluids · doi:10.1063/5.0003702 · Cited by 151
The geometry of chaotic dynamics — a complex network perspective
Donner, R. V., Heitzig, J., Donges, J. F., Zou, Y., Marwan, N., & Kurths, J. (2011) · The European Physical Journal B · doi:10.1140/epjb/e2011-10899-1 · Cited by 150
Wang, M., Zhao, L., Du, R., Wang, C., Chen, L., Tian, L., & Stanley, E. (2018) · Applied Energy · doi:10.1016/j.apenergy.2018.03.148 · Cited by 146
A directed weighted complex network for characterizing chaotic dynamics from time series
Gao, Z., & Jin, N. (2011) · Nonlinear Analysis Real World Applications · doi:10.1016/j.nonrwa.2011.08.029 · Cited by 145
A novel method for forecasting time series based on fuzzy logic and visibility graph
Zhang, R., Ashuri, B., & Deng, Y. (2017) · Advances in Data Analysis and Classification · doi:10.1007/s11634-017-0300-3 · Cited by 143
Evolving networks in the human epileptic brain
Lehnertz, K., Ansmann, G., Bialonski, S., Dickten, H., Geier, C., & Porz, S. (2013) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2013.06.009 · Cited by 135
Visibility graph approach to exchange rate series
Yang, Y., Wang, J., Yang, H., & Mang, J. (2009) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2009.07.016 · Cited by 138
Murugesan, M., & Sujith, R. I. (2015) · Journal of Fluid Mechanics · doi:10.1017/jfm.2015.215 · Cited by 136
Donges, J. F., Heitzig, J., Beronov, B., Wiedermann, M., Runge, J., Feng, Q., Tupikina, L., Stolbova, V., Donner, R. V., Marwan, N., et al. (2015) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4934554 · Cited by 133
A Review on Nonlinear Methods Using Electroencephalographic Recordings for Emotion Recognition
García-Martínez, B., Martínez‐Rodrigo, A., Alcaraz, R., & Fernández‐Caballero, A. (2019) · IEEE Transactions on Affective Computing · doi:10.1109/taffc.2018.2890636 · Cited by 135
Mapping the Alzheimer’s Brain with Connectomics
Xie, T., & Yong He, A. (2012) · Frontiers in Psychiatry · doi:10.3389/fpsyt.2011.00077 · Cited by 129
Carbon price forecasting with complex network and extreme learning machine
Xu, H., Wang, M., Jiang, S., & Yang, W. (2019) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2019.122830 · Cited by 126
Ambiguities in recurrence-based complex network representations of time series
Donner, R. V., Zou, Y., Donges, J. F., et al. (2010) · Physical Review E · doi:10.1103/physreve.81.015101 · Cited by 125
Visibility graph analysis of geophysical time series: Potentials and possible pitfalls
Donner, R. V., & Donges, J. F. (2012) · Acta Geophysica · doi:10.2478/s11600-012-0032-x · Cited by 125
Multi-frequency complex network from time series for uncovering oil-water flow structure
Gao, Z., Yang, Y., Fang, P., Jin, N., Xia, C., & Hu, L.-D. (2015) · Scientific Reports · doi:10.1038/srep08222 · Cited by 124
Limited penetrable visibility graph for establishing complex network from time series
Zhou, T., Jin, N., Gao, Z., & Yue-Bin, L. (2012) · Acta Physica Sinica · doi:10.7498/aps.61.030506 · Cited by 121
Multiscale complex network for analyzing experimental multivariate time series
Gao, Z., Yang, Y., Fang, P., Zou, Y., Xia, C., & Du, M. (2015) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/109/30005 · Cited by 122
Epilepsy Detection From EEG Using Complex Network Techniques: A Review
Supriya, S., Siuly, S., Wang, H., et al. (2021) · IEEE Reviews in Biomedical Engineering · doi:10.1109/rbme.2021.3055956 · Cited by 119
Fault Diagnosis of Rolling Bearing Based on WHVG and GCN
Li, C., Mo, L., & Yan, R. (2021) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.2021.3087834 · Cited by 120
Analysis of seismic sequences by using the method of visibility graph
Telesca, L., & Lovallo, M. (2012) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/97/50002 · Cited by 118
Analytical framework for recurrence network analysis of time series
Donges, J. F., Heitzig, J., Donner, R. V., & Kurths, J. (2012) · Physical Review E · doi:10.1103/physreve.85.046105 · Cited by 115
Using network science and text analytics to produce surveys in a scientific topic
Silva, F. N., Amancio, D. R., Bardosova, M., Costa, L. D. F., & Oliveira, O. N. (2016) · RePEc: Research Papers in Economics · Cited by 117
Ni, X.-H., Zhi-qiang Jiang, A., & Zhou, W. (2009) · Physics Letters A · doi:10.1016/j.physleta.2009.08.041 · Cited by 114
Visibility Graph Based Time Series Analysis
Stephen, M., Gu, C., & Yang, H. (2015) · PLoS ONE · doi:10.1371/journal.pone.0143015 · Cited by 113
Lazcano, A., Herrera, P. J., & Monge, M. (2023) · Mathematics · doi:10.3390/math11010224 · Cited by 122
Feigenbaum Graphs: A Complex Network Perspective of Chaos
Luque, B., Lacasa, L., Ballesteros, F., et al. (2011) · PLoS ONE · doi:10.1371/journal.pone.0022411 · Cited by 113
Self-citationConstructing ordinal partition transition networks from multivariate time series
Zhang, J.-Y., Zhou, J., Tang, M., et al. (2017) · Scientific Reports · doi:10.1038/s41598-017-08245-x · Cited by 111
Geometric detection of coupling directions by means of inter-system recurrence networks
Feldhoff, J. H., Donner, R. V., Donges, J. F., et al. (2012) · Physics Letters A · doi:10.1016/j.physleta.2012.10.008 · Cited by 109
The Number of Confirmed Cases of Covid-19 by using Machine Learning: Methods and Challenges
Ahmad, A., Garhwal, S., Ray, S. K., Kumar, G., Malebary, S. J., & Barukab, O. (2020) · Archives of Computational Methods in Engineering · doi:10.1007/s11831-020-09472-8 · Cited by 110
Identification of influential nodes in complex networks: A local degree dimension approach
Zhong, S., Zhang, H., & Deng, Y. (2022) · Information Sciences · doi:10.1016/j.ins.2022.07.172 · Cited by 108
Boniol, P., & Palpanas, T. (2020) · Proceedings of the VLDB Endowment · doi:10.14778/3407790.3407792 · Cited by 127
AvgNet: Adaptive Visibility Graph Neural Network and Its Application in Modulation Classification
Xuan, Q., Zhou, J., Qiu, K., Chen, Z., Xu, D., Zheng, S., & Yang, X. (2022) · IEEE Transactions on Network Science and Engineering · doi:10.1109/tnse.2022.3146836 · Cited by 106
“[38] proposed the natural Visibility Graph (VG) algorithm for mapping time series into graphs to analyze time series from a new point of view, whose process is shown in Fig.”
BackgroundMethodIrreversibility of financial time series: A graph-theoretical approach
Flanagan, R., & Lacasa, L. (2016) · Physics Letters A · doi:10.1016/j.physleta.2016.03.011 · Cited by 107
Self-citationQian, M., Zhi-qiang Jiang, A., & Zhou, W. (2010) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/43/33/335002 · Cited by 105
Chen, L., Deng, Y., & Cheong, K. H. (2021) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2021.104438 · Cited by 104
Characterizing time series of near-miss accidents in metro construction via complex network theory
Zhou, C., Ding, L., Skibniewski, M. J., et al. (2017) · Safety Science · doi:10.1016/j.ssci.2017.06.012 · Cited by 104
Using network science and text analytics to produce surveys in a scientific topic
Silva, F. N., Amancio, D. R., Bardosova, M., Costa, L. D. F., & Oliveira, O. N. (2016) · Journal of Informetrics · doi:10.1016/j.joi.2016.03.008 · Cited by 132
Wang, W., Mohseni, P., Kilgore, K. L., & Najafizadeh, L. (2021) · IEEE Journal of Biomedical and Health Informatics · doi:10.1109/jbhi.2021.3128383 · Cited by 109
The geometry of chaotic dynamics - a complex network perspective
Donner, R. V., Heitzig, J., Donges, J. F., et al. (2011) · Publication Database PIK (Potsdam Institute for Climate Impact Research (PIK)) · Cited by 102
Sports Injury Forecasting and Complexity: A Synergetic Approach
Fonseca, S. T., Souza, T. R., Verhagen, E. A. L. M., van Emmerik, R. E. A., Bittencourt, N. F. N., Mendonça, L. D. M., de Andrade, A. G. P., Resende, R. A., & Ocarino, J. M. (2020) · Sports Medicine · doi:10.1007/s40279-020-01326-4 · Cited by 112
Network analysis of human heartbeat dynamics
Shao, Z.-G. (2010) · Applied Physics Letters · doi:10.1063/1.3308505 · Cited by 100
Classification of Interbeat Interval Time-Series Using Attention Entropy
Yang, J., Choudhary, G. I., Rahardja, S., & Fränti, P. (2020) · IEEE Transactions on Affective Computing · doi:10.1109/taffc.2020.3031004 · Cited by 102
Testing time series irreversibility using complex network methods
F.Donges, J., Donner, R. V., & Kurths, J. (2013) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/102/10004 · Cited by 100
On the resilience of modern power systems: A complex network perspective
Ma, X., Zhou, H., & Li, Z. (2021) · Renewable and Sustainable Energy Reviews · doi:10.1016/j.rser.2021.111646 · Cited by 98
Mapping stochastic processes onto complex networks
Shirazi, A. H. M., Jafari, G., Davoudi, J., et al. (2009) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2009/07/p07046 · Cited by 98
From the time series to the complex networks: The parametric natural visibility graph
Bezsudnov, I. V., & Snarskii, A. A. (2014) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2014.07.002 · Cited by 98
Ribeiro, M., Henriques, T. S., Castro, L., Souto, A., Antunes, L. F., Santos, C., & Teixeira, A. (2021) · Entropy · doi:10.3390/e23020222 · Cited by 107
Complexity traits and dynamics of tourism destinations
Sainaghi, R., & Baggio, R. (2017) · Tourism Management · doi:10.1016/j.tourman.2017.07.004 · Cited by 95
A characterization of horizontal visibility graphs and combinatorics on words
Gutin, G., Mansour, T., & Simone Severini, B. (2011) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2011.02.031 · Cited by 95
Computational methods of EEG signals analysis for Alzheimer’s disease classification
Vicchietti, M. L., Ramos, F. M., Betting, L. E., & Campanharo, A. S. L. O. (2023) · Scientific Reports · doi:10.1038/s41598-023-32664-8 · Cited by 107
Ravetti, M. G., Carpi, L. C., Gonçalves, B. A., Frery, A. C., & Rosso, O. A. (2014) · PLoS ONE · doi:10.1371/journal.pone.0108004 · Cited by 99
Gao, Z., Zhang, X.-W., Jin, N., et al. (2013) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/103/50004 · Cited by 92
Epileptic seizure detection in EEGs signals based on the weighted visibility graph entropy
Mohammadpoory, Z., Nasrolahzadeh, M., & Haddadnia, J. (2017) · Seizure · doi:10.1016/j.seizure.2017.07.001 · Cited by 92
Price graphs: Utilizing the structural information of financial time series for stock prediction
Wu, J., Xu, K., Chen, X., Li, S., & Zhao, J. (2021) · Information Sciences · doi:10.1016/j.ins.2021.12.089 · Cited by 95
Mapping time series into networks as a tool to assess the complex dynamics of tourism systems
Baggio, R., & Sainaghi, R. (2015) · Tourism Management · doi:10.1016/j.tourman.2015.10.008 · Cited by 90
Ordinal patterns-based methodologies for distinguishing chaos from noise in discrete time series
Zanin, M., & Olivares, F. (2021) · Communications Physics · doi:10.1038/s42005-021-00696-z · Cited by 95
Sánchez-López, J. L., Wang, M., Olivares-Méndez, M. A., Molina, M., & Voos, H. (2018) · Journal of Intelligent & Robotic Systems · doi:10.1007/s10846-018-0809-5 · Cited by 90
Relative Wavelet Entropy Complex Network for Improving EEG-Based Fatigue Driving Classification
Gao, Z., Li, S., Cai, Q., Dang, W., Yang, Y., Mu, C., & Hui, P. (2018) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.2018.2865842 · Cited by 91
Sun, X., SMALL, M. P., Zhao, Y., et al. (2014) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4868261 · Cited by 88
Gao, Z., Dang, W., Mu, C., Yang, Y., Li, S., & Grebogi, C. (2017) · IEEE Transactions on Industrial Informatics · doi:10.1109/tii.2017.2785384 · Cited by 88
Visibility graph analysis on quarterly macroeconomic series of China based on complex network theory
Wang, N., Li, D., & Wang, Q. (2012) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2012.07.054 · Cited by 86
The application of complex network time series analysis in turbulent heated jets
Charakopoulos, A., Karakasidis, T. E., Papanicolaou, P. N., et al. (2014) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4875040 · Cited by 85
Metadata
- Authors
- Lacasa, L., Luque, B., Ballesteros, F., Luque, J., & Nuño, J. C.
- Affiliations
- Universidad Politécnica de Madrid (ES)
- Universitat de València (ES)
- Universitat Politècnica de Catalunya (ES)
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 2008-04
- Volume
- 105
- Issue
- 13
- Pages
- 4972-4975
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC2278201
- OpenAlex
- W2055538060
- Semantic Scholar
- a0c1483e0e34fb9bc1baf929ce892f111e329fa6
- Cited by
- 1,826
- References
- 22
- Citations by year
- 2026: 102 · 2025: 180 · 2024: 149 · 2023: 156 · 2022: 157 · 2021: 151 · 2020: 157 · 2019: 154 · 2018: 137 · 2017: 105 · 2016: 84 · 2015: 60 · 2014: 61 · 2013: 47 · 2012: 51
- FWCI
- 56.61
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- PubMed Central (submittedVersion)
- arXiv (Cornell University)
- Topics
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Complex Systems and Time Series Analysis
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
- Physical Sciences › Computer Science › Signal Processing › Time Series Analysis and Forecasting
- Keywords
- visibility graph, time series, complex networks, scale-free networks, power-law degree distribution, fractality, regular graphs, random graphs, network metrics, time series characterization
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