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.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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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).”
plain- Asserted: passes — The authors put it forward as true.
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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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- Load-bearing: passes — The paper’s conclusions depend on it.
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- 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.”
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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.
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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.
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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.
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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.
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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
“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.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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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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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.
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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.
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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.
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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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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.
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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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- 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).
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Zhang, X., Liu, Q., Li, Q. L., et al. (2024) · Preprints.org · doi:10.20944/preprints202402.0677.v2
Mohammad, A., Almeneem, H. A. A., Asiri, W. M., & Mohamed, I. A. (2024) · World Journal of Biology and Biotechnology · doi:10.33865/wjb.009.02.1283
Measuring Natural Gas Price Feature of Asian-Pacific Market from Complex Network PerspectivePreprint
Su, J., Wang, W., Bai, Y., et al. (2024) · SSRN Electronic Journal · doi:10.2139/ssrn.4805646
Alternative Developing Tools for Economics
Aruka, Y. (2024) · Springer texts in business and economics · doi:10.1007/978-981-97-1382-0_7
EEG Decoding of Auditory Spatial Attention Based on Visibility Graph and Machine Learning
Wang, P., Kausar, T., Li, H., et al. (2024) · doi:10.1145/3653781.3653793
A machine learning ride in the physics theme park: from quantum to biophysics
Requena, B. (2024) · UPCommons institutional repository (Universitat Politècnica de Catalunya) · doi:10.5821/dissertation-2117-409132
Renjini, A., Swapna, M. S., & Sankararaman, S. I. (2024) · Physical and Engineering Sciences in Medicine · doi:10.1007/s13246-024-01455-4
Complex Network: A Potential Tool for Uncloaking Tone Quality of Musical Instruments
Sankararaman, S. I. (2024) · Acoustical Physics · doi:10.1134/s1063771023601231
Coelho, P., Saliba, S., Ramos, L., et al. (2024) · doi:10.5753/ercas.2024.238705
Simone, A., Cesaro, A., & Esposito, G. (2024) · Journal of Water Process Engineering · doi:10.1016/j.jwpe.2024.106107
Xu, Q., Zhu, X., & Gao, N. (2024) · Communications in computer and information science · doi:10.1007/978-981-97-7001-4_28
Statistical Exploration of the Salar de Atacama’s: Brine Measurements of the Basin Wells
Castillo, M. S., & Calderón, F. A. (2024) · Journal of Physics Conference Series · doi:10.1088/1742-6596/2839/1/012019
Complex network-based multistep forecasting model for hyperchaotic time series
Reshmi, L. B., Thumba, D. A., Asokan, K., Kumar, T. K. M., Ramamohan, T. R., & Kumar, K. S. (2024) · Physical review. E · doi:10.1103/physreve.110.044302
Robotic motion planning in surgery
Tian, Y., & Ren, H. (2024) · Elsevier eBooks · doi:10.1016/b978-0-443-13271-1.00032-7
TOPSIS-based identification and analysis of important exam nodes
Xie, W., Liu, X., & Fan, D. (2024) · International Conference on Educational Knowledge and Informatization (EKI) · doi:10.1145/3691720.3691746
Karakasidou, S., Charakopoulos, A., & Zachilas, L. (2024) · AppliedMath · doi:10.3390/appliedmath4040071
Forecasting Time Series through Motif Structure Analysis within Visibility Graph
Wen, T., & Chen, Y. (2024) · International Conference on Automation and Computing (ICAC) · doi:10.1109/icac61394.2024.10718817
Saviola, F., Tambalo, S., Beghini, L., Ferrari, A., Cassone, B., Ville, D. V. D., & Jovicich, J. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.10.30.621153
Complex Network Analysis of Cardiovascular Time Series: Sex Differences in Visibility Graphs
Lavezzo, L., Scilingo, E. P., & Nardelli, M. (2024) · Conference of the European Study Group on Cardiovascular Oscillations (ESGCO) · doi:10.1109/esgco63003.2024.10766996
Dai, Q., Ren, W., Zhang, J., et al. (2024) · IEEE Sensors Journal · doi:10.1109/jsen.2024.3509976
Evaluating Pre-attentive Perception of Visibility Graphs for Representing ECG Signals
Churio, J. F., Sarmiento, W. J., Carvajal, R. E. G., et al. (2024) · Communications in computer and information science · doi:10.1007/978-3-031-75236-0_5
A model of the space of thematic telegram channels based on contextual links
Puchkov, O., Lande, D., & Subach, I. (2024) · Collection Information technology and security · doi:10.20535/2411-1031.2024.12.2.315731
Spatial arrangement of near-wall bursting process and large scales in turbulent boundary layer flows
Shi, L., Zhang, J.-H., Wang, M., et al. (2025) · Physics of Fluids · doi:10.1063/5.0244231
Multiscale topological analysis of virtual currency price series
Li, C., & Bian, A. (2025) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2025.130375
ChartNet : Reducing Subjectivity in Stock Prediction Through Unified Technical Chart Representation
Li, S., Liu, Y., Cheng, F., Wu, J., & Xu, K. (2025) · Expert Systems · doi:10.1111/exsy.13841
Clustering Time Series Data for Personalized Type 1 Diabetes Management
Taştan, A., Escorihuela‐Altaba, C., Garcia‐Tirado, J., & Riesen, K. (2025) · Lecture notes in computer science · doi:10.1007/978-981-97-8705-0_13
Zhang, L., Wang, P., Liu, L., et al. (2025) · International Petroleum Technology Conference · doi:10.2523/iptc-25065-ms
Li, J., & Niu, M. (2025) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2025.130467
Ordinal Structure Network Analysis of Sentence Length Series
姜, 岚. (2025) · Advances in Applied Mathematics · doi:10.12677/aam.2025.142080
Evaluating Machine Learning Algorithms for Time Series Classification Using Complex Network Features
Duc, Q. T., Van, H. N., & Do, T.-A. (2024) · International Conference on Advanced Technologies for Communications · doi:10.1109/atc63255.2024.10908346
Anomaly Detection of Power Time Series Data with Multi-Head Graph Attention Networks
Shen, W., Dai, T., Chen, Z., et al. (2024) · International Conference on Artificial Intelligence and Computer Engineering (ICAICE) · doi:10.1145/3716895.3716998
Telesca, L., Panebianco, S., Serlenga, V., et al. (2025) · Fractal and Fractional · doi:10.3390/fractalfract9040208
Zhu, X., Wang, B., Chen, J., et al. (2025) · Shock and Vibration · doi:10.1155/vib/4851847
Forecasting Stock Price Patterns with a Rising Visibility Graph Based Method
Zeng, Z., & Chen, Y. (2025) · Studies in computational intelligence · doi:10.1007/978-3-031-82431-9_15
Classification of Sleep Stages Based on Quantile Graphs from Mouse EEG
Koyama, K., Sakaguchi, M., & Ohnishi, T. (2025) · Studies in computational intelligence · doi:10.1007/978-3-031-82439-5_11
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Moraes, J. T., & Ferreira, S. C. (2025) · Physical review. E · doi:10.1103/physreve.111.044302
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Jalapally, P., & Izudheen, S. (2025) · Springer proceedings in mathematics & statistics · doi:10.1007/978-981-96-1505-6_5
Next Higher Point: Two Novel Approaches for Computing Natural Visibility Graphs
Daniel, P., Silva, V. F., & Ribeiro, P. (2025) · Studies in computational intelligence · doi:10.1007/978-3-031-82427-2_22
Ahmed, A., Subba, N., Biswas, T., Alshehri, A. A., Tawfik, A. N., & Haldar, P. K. (2025) · Canadian Journal of Physics · doi:10.1139/cjp-2024-0047
Assessing the interactions between time series signals using weighted horizontal visibility graphs
Teymourlouei, A., Reggia, J. A., & Gentili, R. J. (2025) · Journal of Physics Complexity · doi:10.1088/2632-072x/add3a8
RELATIVE NODE DEGREES AND LINK LENGTHS OF PARAMETRIC THUE–MORSE NETWORK
Sun, T. C., & Niu, M. (2025) · Fractals · doi:10.1142/s0218348x25500732
Detecting Pain During Cognitive Tasks via Visibility Graphs of Cortical Signals
Subramanian, A., & Najafizadeh, L. (2025) · IEEE International Symposium on Biomedical Imaging (ISBI) · doi:10.1109/isbi60581.2025.10981165
Graph-Based Features and Refined Diffusion Models for Stock Price Prediction
Nguyen, C. N., Vuong, K. M., & Pham, T. K. D. (2025) · Lecture notes in networks and systems · doi:10.1007/978-3-031-90606-0_22
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Zeng, Z., & Chen, Y. (2025) · Forecasting · doi:10.3390/forecast7020026
Yu, Q., Yin, C., Cao, N., et al. (2025) · International Conference on Energy, Electrical and Power Engineering (CEEPE) · doi:10.1109/ceepe64987.2025.11034217
GazeMotif: A Gaze Speed Motif based Learning Behaviour Analysis Framework for Video Learning
Li, H., Yang, Z., Xie, Y., et al. (2024) · International Conference on Mobility, Sensing and Networking (MSN) · doi:10.1109/msn63567.2024.00176
Structure of Autocorrelation in Time Series
Ren, H., Zhang, G., & Feng, B. (2025) · International Conference on Informatics Education and Computer Technology Applications (IECA) · doi:10.1145/3732801.3732871
Karakasidis, T. E., & Charakopoulos, A. (2025) · Springer eBooks · doi:10.1007/978-3-031-92628-0_4
Complex Network Methods, PALS, ATR-FTIR and EPR Study of Photopolymerization
Kavetskyy, T. S., Zubrytska, O., Stievenard, M., et al. (2025) · NATO science for peace and security series. B, Physics and biophysics · doi:10.1007/978-94-024-2316-7_19
Chaotic Time Series Analysis: A View of Transition Networks
Zheng, Z., & Xu, P. (2025) · Journal of Systems Science and Complexity · doi:10.1007/s11424-025-4300-7
Dengue Serotypes Cyclicity Evidenced by the Impact-Frequency Histogram of the Visibility Graph
Lima, L. L., & Atman, A. P. F. (2025) · Springer proceedings in complexity · doi:10.1007/978-3-031-93619-7_7
Adversarial influence maximization algorithm based on node local influence
Zhan, X., Xu, Y., Qingtao, P. A. N., et al. (2025) · Scientia Sinica Informationis · doi:10.1360/ssi-2024-0380
Ramírez-Rojas, A., Moreno, P. R. C., Reyes-Ramírez, I., et al. (2025) · Applied Sciences · doi:10.3390/app15168775
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.
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