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.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Verification
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.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“( 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).”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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 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.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- 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.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- Also stated in: § Resumen · p. 1 · 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
“( ii ) undirected: the way the algorithm is built up, there is no direction defined in the links.”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“( i ) connected: each node sees at least its nearest neighbors (left and right).”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“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.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“that is, the degree distribution related to the C-nodes is a power law.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“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.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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
“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.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- 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.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- 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”
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- 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
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
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.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
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.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
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.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
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.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
- Not matched
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
Items 1,401–1,500 of 1,826
Tabar, M. R. R. (2019) · Understanding complex systems · doi:10.1007/978-3-030-18472-8_20 · Cited by 1
Liu, D., Li, C., Zhao, D., et al. (2019) · Energy Science & Engineering · doi:10.1002/ese3.467 · Cited by 1
A Novel Method of Radar Antenna Scan Pattern Recognition Using Visibility Graph
Wan, T., Fu, X., Jiang, K., et al. (2019) · Journal of Physics Conference Series · doi:10.1088/1742-6596/1325/1/012162 · Cited by 1
Temperature time series analysis at Yucatan using natural and horizontal visibility algorithms
Rosales-Pérez, J. A., Canto‐Lugo, E., Valdés-Lozano, D. S., et al. (2019) · PLoS ONE · doi:10.1371/journal.pone.0226598 · Cited by 1
Recurrence Network-Based Approach to Distinguish Between Chaotic and Quasiperiodic Solution
Mohan, A., Vijesh, V., Thumba, D. A., et al. (2020) · Communications in computer and information science · doi:10.1007/978-981-15-4828-4_30 · Cited by 1
Bhaduri, S., & Bhaduri, A. (2020) · Physics · doi:10.3390/physics2030025 · Cited by 1
Графи видимості — інструмент мережевого аналізу рядів вимірів
Snarskii, A. A., & Lande, D. (2013) · Реєстрація зберігання і обробка даних · doi:10.35681/1560-9189.2013.15.2.103376 · Cited by 1
Tsiotas, D., Magafas, L., & Hanias, M. P. (2020) · Physics · doi:10.3390/physics2040036 · Cited by 1
Motif-Assisted Load Classification: Time Series Analysis Using Complex Network Theory
Qi, M., Mei, L., Li, Z., et al. (2021) · IEEE International Electrical and Energy Conference (CIEEC) · doi:10.1109/cieec50170.2021.9510294 · Cited by 1
Analysis of Stock Price Data: Determinition of The Optimal Sliding-Window Length
Liu, X., Yuan, X., Liu, C., et al. (2021) · Frontiers in Physics · doi:10.3389/fphy.2021.741106 · Cited by 1
Cardiorespiratory alterations in a newborn ovine model of systemic viral inflammation
Nault, S., Tremblay, S., Imane, R., Omar, S. A., Nadeau, C., Samson, N., Creuze, V., Carrault, G., Pladys, P., & Praud, J. (2022) · Pediatric Research · doi:10.1038/s41390-022-01958-4
Graph regression for pressure peak prediction in fracturing processes
Zhang, W., He, Y., Li, P., et al. (2022) · Journal of Petroleum Science and Engineering · doi:10.1016/j.petrol.2022.110323 · Cited by 1
Bianconi, G. (2018) · Oxford University Press eBooks · doi:10.1093/oso/9780198753919.003.0009 · Cited by 1
Gao, Z., Jin, N., & Wang, W.-X. (2013) · SpringerBriefs in applied sciences and technology · doi:10.1007/978-3-642-38373-1_1 · Cited by 1
Walker, D. M., Corrêa, D., & Algar, S. D. (2022) · Expert Systems with Applications · doi:10.1016/j.eswa.2022.118586 · Cited by 1
Kharajinezhadian, F., Yazdani, F., Isfahani, P. P., & Kavousi, M. (2022) · SN Computer Science · doi:10.1007/s42979-022-01431-3 · Cited by 1
Binary Classification of Mammograms Using Horizontal Visibility Graph
Ghosh, A., Ranjan, P., Chilamkurthy, N. S., et al. (2022) · Lecture notes in electrical engineering · doi:10.1007/978-981-19-6581-4_27 · Cited by 1
金, 晓. (2022) · Advances in Applied Mathematics · doi:10.12677/aam.2022.1111804 · Cited by 1
Non-Negative Kernel Graphs for Time-Varying Signals Using Visibility Graphs
Bozkurt, E., & Ortega, A. (2022) · 2022 30th European Signal Processing Conference (EUSIPCO) · doi:10.23919/eusipco55093.2022.9909594 · Cited by 1
EMD and Horizontal Visibility Graph Based Disease Tagging for Covid-Positive Chest Radiographs
Chavan, N., Ranjan, P., Shrivastav, K. D., & Janardhanan, R. (2022) · Springer series on bio- and neurosystems · doi:10.1007/978-3-031-10031-4_14 · Cited by 1
Construction of semantic networks and determining the degree of divergence of texts
Lande, D., & Dmytrenko, O. (2022) · INFORMATION AND LAW · doi:10.37750/2616-6798.2022.2(41).270362 · Cited by 1
Beltran, E., Barocio, E., & del Puerto-Flores, D. (2023) · Elsevier eBooks · doi:10.1016/b978-0-32-399904-5.00012-0 · Cited by 1
Wang, W., & Najafizadeh, L. (2022) · Asilomar Conference on Signals, Systems and Computers (ACSSC) · doi:10.1109/ieeeconf56349.2022.10051933 · Cited by 1
Quantifying time series complexity by multi-scale transition network approaches
Wang, X., Tang, M., Guan, S., et al. (2023) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2023.128845 · Cited by 1
Analysis of COVID-19 Offensive Tweets and Their Targets
Liao, S., Okpala, E., Cheng, L., Li, M., Vishwamitra, N., Hu, H., Luo, F., & Costello, M. (2023) · ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD) · doi:10.1145/3580305.3599773 · Cited by 3
A sound frequency ridge positioning model oriented to mine equipment
Ye, T., Peng, T., & Li, J. (2023) · Journal of Vibration and Control · doi:10.1177/10775463231193470 · Cited by 1
Image Visibility Graph Analysis of the Eye Disease Images
Wu, D., Ma, Z., Yang, X., Jiang, G., Chen, Y., & Ma, L. (2023) · International Congress on Image and Signal Processing (CISP) · doi:10.1109/cisp-bmei60920.2023.10373331 · Cited by 1
Pei, L., Liu, J., & Cai, Z. (2024) · AIP Advances · doi:10.1063/5.0156080 · Cited by 1
A complex network analysis on the eigenvalue spectra of random spin systems
Xue, Q., & Rao, W.-J. (2024) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2024.129572 · Cited by 1
Global Synchronization Measure Applied to Brain Signals Data
Dhamo, X., Kalluçi, E., Dray, G., et al. (2024) · Studies in computational intelligence · doi:10.1007/978-3-031-53503-1_35 · Cited by 1
Andrzejewska, M., Wróblewski, T., Cygan, S., et al. (2024) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0178750 · Cited by 1
Multiscale Irreversibility Analysis of Time Series Based on Permutation Jensen–Shannon Distance
Fan, Q., Song, J., & Li, D. (2024) · Fluctuation and Noise Letters · doi:10.1142/s0219477525500130 · Cited by 1
AMANO, S., Kawada, T., Fukuda, S., et al. (2024) · Proceedings of the Combustion Institute · doi:10.1016/j.proci.2024.105702 · Cited by 1
A novel approach to detecting epileptic patients: complex network-based EEG classification
Olgun, N., & Özkaynak, E. (2024) · Journal of Complex Networks · doi:10.1093/comnet/cnae044 · Cited by 1
Yang, Y.-H., Liu, Y.-L., & Shao, Y.-H. (2024) · Fluctuation and Noise Letters · doi:10.1142/s021947752550021x · Cited by 1
Sadoun, M. S. N., & Laleg‐Kirati, T. (2024) · doi:10.1109/embc53108.2024.10782524 · Cited by 1
Manipulating Time Series Irreversibility Through Continuous Ordinal Patterns
Zanin, M. (2024) · Symmetry · doi:10.3390/sym16121696 · Cited by 1
Applied DNA visibility graphs: Understanding DNA structure-function relationship in genomics
Kosmidis, K. (2025) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2025.130436 · Cited by 1
Detecting extreme values in time series based on bar visibility
Katsouda, M., & Boutsinas, B. (2025) · International Journal of Data Science and Analytics · doi:10.1007/s41060-025-00758-3 · Cited by 1
A novel baseline perspective visibility graph for time series analysis
Ni, H., Zi-Jie, S., Qin, J., Wu, Y., Shi-Le, Q., & Ming, S. (2025) · Chinese Physics B · doi:10.1088/1674-1056/adce9a · Cited by 1
Multi time-delay fuzzy dispersion network analysis of nonlinear time series
Geng, B., Wang, H., Yan, Y., et al. (2025) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2025.109078 · Cited by 1
Exploring complexity measures for analysis of solar wind structures and streams
Koikkalainen, V., Kilpua, E. K. J., Good, S., et al. (2025) · Nonlinear processes in geophysics · doi:10.5194/npg-32-309-2025 · Cited by 1
A Complex Network of Well Log based on Visibility Graph
Li, X., Chen, L., & Xiao, J. (2014) · International Journal of Signal Processing Image Processing and Pattern Recognition · doi:10.14257/ijsip.2014.7.2.34 · Cited by 1
Multiscale structure of time series revealed by the monotony spectrum
Vamoş, C. (2017) · Physical review. E · doi:10.1103/physreve.95.033310 · Cited by 1
A New Epileptic Seizure Detection Method Based on Degree Centrality and Linear Features
Liu, H., Meng, Q., Wei, Y., et al. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-59081-3_51 · Cited by 1
The Structure of Single Networks
Bianconi, G. (2018) · Oxford University Press eBooks · doi:10.1093/oso/9780198753919.003.0002 · Cited by 1
Network Based Periodicity Detection of a Time Series
Vijesh, V., Drisya, G. V., & Kumar, K. S. (2018) · IEEE Recent Advances in Intelligent Computational Systems · doi:10.1109/raics.2018.8634897 · Cited by 1
Iacobello, G., Ridolfi, L., Marro, M., et al. (2019) · Springer proceedings in physics · doi:10.1007/978-3-030-22196-6_34 · Cited by 1
Nonuniversality of the horizontal visibility graph in inferring series periodicity
Xiong, H., Shang, P., & He, J. (2019) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2019.122234 · Cited by 1
Evaluation of missing ordinal pattern and its fractional distribution entropy
Rong, L., & Shang, P. (2019) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2019.122317 · Cited by 1
Bayrakdar, N., Gemmetto, V., & Garlaschelli, D. (2023) · Entropy · doi:10.3390/e25050828 · Cited by 1
Novel Automatic Epilepsy Detection Method Multi-weight Transition Network
Li, Y., Meng, Q., Wu, P., et al. (2019) · doi:10.1109/embc.2019.8856708 · Cited by 1
Stability of exoplanetary systems retrieved from scalar time series
Kovács, T. (2019) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stz3219 · Cited by 1
The evolution of turbulent wake examined using the horizontal visibility graph
Wu, H., & Tao, X. (2020) · AIAA SciTech Forum · doi:10.2514/6.2020-0353 · Cited by 1
Time-Series and Network Analysis in Quantum Dynamics: Comparison with Classical Dynamics
Laha, P., Lakshmibala, S., & Balakrishnan, V. (2020) · International Journal of Theoretical Physics · doi:10.1007/s10773-020-04610-1 · Cited by 1
Визначення вагових значень зв’язків у мережі термінів
Lande, D., & Dmytrenko, O. (2019) · Реєстрація зберігання і обробка даних · doi:10.35681/1560-9189.2019.21.4.199357 · Cited by 1
Cardoso-Pereira, I., Borges, J. B., Barros, P. H., et al. (2019) · doi:10.5753/sbrc.2019.7391 · Cited by 1
Ahmed, A., Subba, N., Haldar, P. K., & Tawfik, A. N. (2021) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-021-01078-8 · Cited by 1
Comparison of different seismic networks efficiencies in earthquake forecasting models
Dehkordi, S. H., Ahmadian, F., Zaré, M., et al. (2021) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-021-01783-4 · Cited by 1
Complex Network Approach to Thermoacoustic Systems
Sujith, R. I., & Pawar, S. A. (2021) · Springer series in synergetics · doi:10.1007/978-3-030-81135-8_11 · Cited by 1
Naghipour, L., Aalami, M. T., & Nourani, V. (2022) · International Journal of Climatology · doi:10.1002/joc.7547 · Cited by 1
VarioGram – A colorful time-graph representation for time series
Serkan, A. K. S. U., & Türker, İ. (2022) · Bilgi ve İletişim Teknolojileri Dergisi · doi:10.53694/bited.1177504 · Cited by 1
Padilla, R. V. V., Rodríguez‐Vázquez, K., Vázquez-Hernández, M., et al. (2022) · World Congress on Medical Physics and Biomedical Engineering, September 7 - 12, 2009, Munich, Germany · doi:10.1007/978-3-031-18256-3_3 · Cited by 1
On the Degree Distribution of Haros Graphs
Calero-Sanz, J. (2022) · Mathematics · doi:10.3390/math11010092 · Cited by 1
Cuff-Less blood pressure estimation from Photoplethysmography via weighted visibility graph
Liu, Y., Yu, J., & Mou, H. (2022) · Cross Strait Radio Science & Wireless Technology Conference (CSRSWTC) · doi:10.1109/csrswtc56224.2022.10098292 · Cited by 1
Looking into the future of complex dynamic systems
Baggio, R. (2015) · Munich Personal RePEc Archive (Ludwig Maximilian University of Munich) · Cited by 1
Markov-Binary Visibility Graph: a new method for analyzing Complex SystemsPreprint
Sadra, Y., ArastehFard, Z., & Ahadpour, S. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1110.4906 · Cited by 1
Words as block of notes and Zipf law in music using visibility algorithmPreprint
Islas, M. S. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1706.09535 · Cited by 1
Time series data mining using complex networks
Ferreira, L. N. (2018) · Digital Library of Theses and Dissertations (Universidade de São Paulo) · doi:10.11606/t.55.2018.tde-01022018-144118 · Cited by 1
Gund, J., & Singh, R. K. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/569244 · Cited by 1
Time Series Analysis of S&P 500 Index: A Horizontal Visibility Graph ApproachPreprint
Vamvakaris, M. D., Pantelous, A. A., & Zuev, K. M. (2017) · SSRN Electronic Journal · doi:10.2139/ssrn.3031781 · Cited by 1
Tagliabue, J., Lacasa, L., Greco, C., et al. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1907.02797 · Cited by 1
Self-citationPyIOmica: Longitudinal Omics Analysis and ClassificationPreprint
Domanskyi, S., Piermarocchi, C., & Mias, G. I. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/708941 · Cited by 1
Cardoso-Pereira, I., Borges, J. B., Barros, P. H., Loureiro, A. A. F., Rosso, O. A., & Ramos, H. S. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2007.08687 · Cited by 1
Моделювання мультиплексних мереж
Соловйов, В. М., & Соловйова, В. В. (2016) · doi:10.31812/0564/1253 · Cited by 1
Persistent Homology of Weighted Visibility Graph from Fractional Gaussian Noise.Preprint
Masoomy, H., Askari, B., Najafi, M. N., & Movahed, M. S. (2021) · arXiv (Cornell University) · Cited by 1
da Silva, I. B. S. T. T., Borges, J. B., Barros, P. H., Loureiro, A. A. F., Rosso, O. A., & Ramos, H. S. (2021) · Research Square · doi:10.21203/rs.3.rs-348558/v1 · Cited by 1
Construction Cost Index Forecasting: A Multi-feature Fusion ApproachPreprint
Zhan, T., He, Y., & Xiao, F. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2108.10155 · Cited by 1
Counting Horizontal Visibility GraphsPreprint
Juhnke‐Kubitzke, M., Köhne, D., & Schmidt, J. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2111.02723 · Cited by 1
Mapping Dynamics into Graphs. The Visibility Algorithm
Núñez, Á. M. (2014) · doi:10.20868/upm.thesis.33779 · Cited by 1
Zhang, L., Zhou, M., Liu, Y., et al. (2024) · Research Square · doi:10.21203/rs.3.rs-4436890/v1 · Cited by 1
Bao Game Analysis Via Visibility Graphs: A Complex Network Approach to Cultural Gameplay DynamicsPreprint
Semba, S. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5362580 · Cited by 1
Wang, N., Li, D., & Wang, Q. (2012) · Lecture notes in electrical engineering · doi:10.1007/978-3-642-25781-0_40
Threshold grouping method to derive complex networks from time series
Murugesan, M., & Sujith, R. I. (2014) · Network and complex systems
A community evolution model based on visibility graph
Hong, W., & Yan-shen, S. (2015) · Chinese Control Conference (CCC) · doi:10.1109/chicc.2015.7259946
Liu, G. (2015) · Digital Commons - University of South Florida (University of South Florida)
Reliable Detection of Malignant Ventricular Arrhythmias Based on Complex Network Theory
Yang, D., & Li, X. (2013) · Lecture notes in computer science · doi:10.1007/978-3-642-36669-7_25
The roles of small-world and degree heterogeneity on evolutionary behavior networks
Yang, Y., Li, X., & Rong, Z. (2010) · doi:10.1109/iscas.2010.5537718
Wang, J., Wen, C., & Wang, X. (2014) · Mathematical Structures in Computer Science · doi:10.1017/s0960129512000503
Complex Networks from Colored Gaussian Noise
Shao, Z.-G., Ai, B.-Q., Yang, L., et al. (2011) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.80.074001
Detecting growth of groups in networks by using a transformation method from networks to time series
Shimada, Y., Hirata, Y., Ikeguchi, T., et al. (2014) · IEICE Proceeding Series · doi:10.15248/proc.2.231
Identifying nonlinearities by time-reversal asymmetry of vertex properties in visibility graphs
Donner, R. V., & Donges, J. F. (2014) · IEICE Proceeding Series · doi:10.15248/proc.1.435
Liao, F., & Jan, Y. (2012) · Journal of Biomedical Graphics and Computing · doi:10.5430/jbgc.v2n1p47
Time-series network analysis for detecting cardiac autonomic neuropathy using RR interval data
Karmakar, C. K., Khandoker, A. H., Jelinek, H. F., et al. (2013) · Charles Sturt University Research Output (CRO)
Meng, Q., Wang, F., Zhou, W., et al. (2013) · Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC) · doi:10.1109/apsipa.2013.6694356
Xiang, R., & SMALL, M. P. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1406.4714
Dynamic Multi-relational Networks Integration and Extended Link Prediction Method
Wang, H., & Sun, Y. (2015) · Lecture notes in computer science · doi:10.1007/978-3-319-23862-3_19
Exploring complex networks by means of two-variable time series of vertex observablesPreprint
Oświȩcimka, P., Livi, L., & Drożdż, S. (2016) · arXiv (Cornell University)
Zhang, Q. (2016) · Canadian social science
Volatilities and Correlations in the Stock Market During the Global Financial CrisisPreprint
Tan, C. H., & Ding, D. (2015) · SSRN Electronic Journal · doi:10.2139/ssrn.2647814
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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-21, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-21 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
