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 1,701–1,800 of 1,826
Peng, B., & Gao, S. (2025) · Systems Science & Control Engineering · doi:10.1080/21642583.2025.2546844
Yue, L., Han, S., & Wang, J. (2025) · Engineering Computations · doi:10.1108/ec-10-2024-0916
Learning sequential data with coarsened visibility graphs and graph neural networksPreprint
Fernandes, J. M., Cunha, T. M., Martins, M. M., et al. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5459119
A universal scaling law in complex systems
Fang, Q., Cai, X., Zhou, L., et al. (2025) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2025.117183
A Geometric Based Functional Connectivity Analysis for Spatiotemporal Time Series Modelling
Ghahremani-Gol, H., & Mohammadian, A. (2025) · Signal Image and Video Processing · doi:10.1007/s11760-025-04692-6
Diagnosis of Flame Instabilities Using Physics-Based and Data-Driven Approaches
De, S., Bhattacharya, C., Mondal, S., et al. (2025) · Green energy and technology · doi:10.1007/978-981-96-8602-5_15
Multiscale topological analysis of cryptocurrency price series
Fang, Q., Weng, T., Wu, M., et al. (2025) · International Journal of Modern Physics C · doi:10.1142/s0129183126500415
Analysis of persistent and antipersistent time series with the Visibility Graph method
Cádiz, M., Gallo-Méndez, I., Moya, P. S., et al. (2025) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2025.117280
Use of visibility graphs for analysis of computed tomography soil images
Vilela, N. S., Aguiar, J. D. A., Stošić, T., et al. (2025) · Acta Scientiarum Agronomy · doi:10.4025/actasciagron.v47i1.72576
Bao game analysis via visibility graphs: A complex network approach to cultural gameplay dynamics
Semba, S. (2025) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2025.131063
Learning Across Modalities: A Systematic Survey of Multimodal Models for Financial AnalysisPreprint
D’Amico, S., Mercorio, F., Nobani, N., et al. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5682250
Detecting seasonal snow transitions in SAR time series with Horizontal Visibility Graphs
Beltramone, G., Frery, A. C., Scavuzzo, C. M., et al. (2025) · Remote Sensing Applications Society and Environment · doi:10.1016/j.rsase.2025.101772
Modeling public attention behavior on badminton’s ecosystem evolution via complex network theory
Liang, Y., Xu, Y., Gu, R., et al. (2025) · Frontiers in Sports and Active Living · doi:10.3389/fspor.2025.1647207
Pérez, S. I., & Herrero, R. C. (2025) · IntechOpen eBooks · doi:10.5772/intechopen.1011930
Hybrid Visibility Graph and Long Short Term Memory for Schizophrenia Detection
Belhadi, A., Djenouri, Y., Lind, P. G., et al. (2025) · doi:10.1109/ijcnn64981.2025.11228894
STVGN: Spatiotemporal Visibility Graph for Short-Term Traffic Speed Prediction
Zhang, Y., Ren, X., Chen, T., et al. (2025) · doi:10.1109/ijcnn64981.2025.11229377
Local Reception Graph Network for Automatic Modulation Recognition in Cognitive RadiosPreprint
Zhou, C., Yang, M., Meng, H., & Yuan, S. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5774594
Quality Assessment of Despeckling Filters Based on Ratio Images and Visibility Graphs
Vásquez-Salazar, R. D., Cardona-Mesa, A. A., Frery, A. C., et al. (2025) · IEEE International Geoscience and Remote Sensing Symposium (IGARSS) · doi:10.1109/igarss55030.2025.11242343
Kırmızıbekmez, A. M., Önder, A., Ozdemir, M. Y., Gurerk, G., Aydın, S., Eryiğit, Ö. Y., Güloğlu, M. O., & Kara, İ. (2025) · Scientific Reports · doi:10.1038/s41598-025-29256-z · Cited by 1
Uncovering Hidden Market Dynamics via Quantile Graph Structural Significance
Nie, C.-X. (2025) · Computational Economics · doi:10.1007/s10614-025-11188-5
Ni, H., Yu-Fei, D., 吴, Y. 烨. W., 秦, J.-L. 姣. Q., & Initiative, A. D. N. (2025) · Chinese Physics B · doi:10.1088/1674-1056/ae2670
Copula-based analytical results of horizontal visibility graphs for correlated time series
Lee, J.-M., & Jo, H.-H. (2025) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2025.135058
Yao, M., Jiang, J., & Tan, L. (2025) · IEEE Annual Ubiquitous Computing, Electronics & Mobile Communication Conference (UEMCON) · doi:10.1109/uemcon67449.2025.11267697
Xie, Y., Shen, M., Dang, Y., & Furuya, N. (2025) · Journal of Building Engineering · doi:10.1016/j.jobe.2025.114790
Lin, X., Lu, Q., An, Y., et al. (2025) · ASCE International Conference on Computing in Civil Engineering (i3CE) · doi:10.1061/9780784486122.016
Regional heatwave variations in China pose a threat to summer grain yields
Zhang, P., Dai, E., Wu, C., et al. (2025) · Food Security · doi:10.1007/s12571-025-01599-5
Network-based characterization of time series and its application to signal classification
Mi, Y., & Lin, A. (2025) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2025.117300
Zhao, Z., & Wang, F. (2025) · Safety Science · doi:10.1016/j.ssci.2025.107073
Quality Assessment of Despeckling Filters Based on the Analysis of Ratio Images
Vásquez-Salazar, R. D., Puche, W. S., Frery, A. C., et al. (2025) · Remote Sensing · doi:10.3390/rs17244048
Liu, S., Zhu, M., Wang, M., et al. (2025) · Applied Soft Computing · doi:10.1016/j.asoc.2025.114535
Díaz, L. R. M., Pinzon-Arenas, J. O., Constable, P. A., & Posada-Quintero, H. F. (2025) · Wearable and Implantable Body Sensor Networks · doi:10.1109/bsn66969.2025.11337467
Gargano, A., Machkour, J., Nardelli, M., et al. (2025) · IEEE International Conference on Metrology for eXtended Reality, Artificial Intelligence and Neural Engineering (MetroXRAINE) · doi:10.1109/metroxraine66377.2025.11339922
Modak, S., Halder, S., & Chatterjee, S. (2026) · IEEE Sensors Letters · doi:10.1109/lsens.2026.3657220
Zhang, L., Zhao, H., Wang, Q., Wu, Y., Dai, H., & Zhu, H. (2025) · International Conference on Wireless Communications and Signal Processing (WCSP) · doi:10.1109/wcsp68525.2025.1010363 · Cited by 1
Evaluating Graph-Based Representations of ATR-FTIR Data Using Complex Networks
Gama, B. C., Silva, R. S., Caixeta, D. C., et al. (2026) · Lecture notes in computer science · doi:10.1007/978-3-032-15990-8_12
VCRec: Visibility graph and convolutional neural networks for sequential recommendation
Li, H., & Wang, J. (2026) · Information Sciences · doi:10.1016/j.ins.2026.123153
de Jesus, L. C., Fernández-Navarro, F., & Carbonero-Ruz, M. (2026) · Mathematics · doi:10.3390/math14030538
Kumari, R., Aggarwal, A. R., & Gupta, A. (2026) · International Journal of Mathematics for Industry · doi:10.1142/s2661335226500024
Chen, G., Li, F., Wang, R., et al. (2026) · Atmosphere · doi:10.3390/atmos17020226
Number of spanning trees as an indicator of critical phenomena: When Kirchhoff meets Ising
da Silva, R., Fernandes, H. A., Gomes, P. F., et al. (2026) · Physical review. E · doi:10.1103/kzxs-9pv8
Bonalumi, F., Burattini, M., Statello, R., Hu, M., Hoang, M. L., Delmonte, N., Caputo, A., Montanini, B., Muzio, F. P. L., Pinelli, S., et al. (2026) · Archives of Toxicology · doi:10.1007/s00204-026-04337-8
Visibility graph approach to characterize planetary transit signatures: A case study on OGLE IV data
Jain, A. B., Kartha, M. J., & Prajapati, Y. (2026) · New Astronomy · doi:10.1016/j.newast.2026.102548
Ye, S., Zhao, X., Dai, P., et al. (2026) · Journal of Environmental Management · doi:10.1016/j.jenvman.2026.129359
Information‐Driven Modeling of Energy Markets: An Unbalanced Wasserstein Barycenter Approach
Mari, C., Mari, E., & Baldassari, C. (2026) · Applied Stochastic Models in Business and Industry · doi:10.1002/asmb.70080
5G Traffic Classification Based on LPVG-GCN
Sun, K., & Qu, T. (2025) · doi:10.1109/icicn67355.2025.11430485
Time series classification using visibility graph and persistent homology
Valderama, D. E., Julian, M. A. F., & Lara, M. L. D. D. (2026) · AIP conference proceedings · doi:10.1063/5.0312988
Research on Fault Diagnosis for Variable-Speed Bearings Using VG and GAF Algorithms
Wang, X., Zhang, D., & Wang, J. (2025) · doi:10.1109/aibdf67964.2025.11440796
A unified time series classification framework via adaptive Gaussian image representation
Ren, X., Li, D., Gao, X., & Chan, W. K. V. (2026) · Scientific Reports · doi:10.1038/s41598-026-44760-6
Characterization of Soil CO2 Flux from an Active Volcano Through Visibility Graph Analysis
Scudero, S., Liuzzo, M., D’Alessandro, A., et al. (2026) · Applied Sciences · doi:10.3390/app16073134
A Straightforward Approach to Construct “Lightweight” Token Graphs from Transformers
Pimentel, J., Amorim, J., & Rudzicz, F. (2026) · Computational Linguistics · doi:10.1162/coli.a.618
Classification of signals and graphs by algebraic spectral approaches
Bay-Ahmed, H.-A. (2018) · theses.fr (ABES) · doi:10.70675/3497f88dzfe6ez46b4z90b3z3710b16c21c1
Distinguishing time series generated by different intrinsic dynamics using quantile graphs
Nie, C.-X. (2026) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2026.110002
Towards Robust Deep Learning Methods for Time Series Data and their Applications
Kosma, C. (2023) · theses.fr (ABES) · doi:10.70675/dd69d4f4ze1efz446czb4dfz2eb82ce78aca
Zhang, Y., & Zeng, Q. (2026) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2026.118334
Zhu, Y., & Li, P. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.6569380
Higher-order linegraph topology for intrusion detection: a hypergraph approach
Manjunatha, K. K. H., Pérez, S. I., & Criado, R. (2026) · International Journal of Data Science and Analytics · doi:10.1007/s41060-026-01102-z
Telesca, L., Abate, N., & Lasaponara, R. (2026) · Journal of Physics Complexity · doi:10.1088/2632-072x/ae6218
Jiang, R., Shang, P., & Zhang, B. (2026) · Applied Mathematical Modelling · doi:10.1016/j.apm.2026.117021
Supriya, S., Sidnal, N. S., & Jan, T. (2026) · Lecture notes in computer science · doi:10.1007/978-981-95-6304-3_7
Liu, C., Zhang, P., Rong, D., et al. (2026) · Lecture notes in electrical engineering · doi:10.1007/978-981-95-7676-0_47
Graph-theoretic modeling of double pendulum trajectories
Bakim, S., Özalan, N. U., & Gülbahçe, E. (2026) · Physica Scripta · doi:10.1088/1402-4896/ae67b9
Study of sequential emotional dynamics: a LSDVG approach with reduced electrode configuration
Farman, S. A., Sudhamayee, K., & Manimaran, P. (2026) · Cognitive Neurodynamics · doi:10.1007/s11571-026-10461-z
A new lung disorder detection model based on graphene pattern using respiratory sounds
Barua, P. D., Göktaş, Ö. F., Doğan, Ş., Bayğın, N., Bayğın, M., Salvi, M., Tuncer, T., Tan, R., & Acharya, U. R. (2026) · Speech Communication · doi:10.1016/j.specom.2026.103414
Vangelis, H., Spiliotis, K., & Spiliotis, M. (2026) · Water Resources Management · doi:10.1007/s11269-026-04656-6
Detecting stochasticity in discrete signals via nonparametric excursion theorem
Tanweer, S., & Khasawneh, F. A. (2026) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0324348
Liu, J.-L., Yang, C.-Y., Yu, Z.-G., et al. (2026) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2026.131656
Yan, H., & Zhu, F. (2026) · Egyptian Informatics Journal · doi:10.1016/j.eij.2026.100986
Horizontal Visibility Graph-Based Time Series Forecasting
Farkas, F. (2026) · SEFBIS Journal · doi:10.14267/sefbis.2026.01
AEVGNet: Angle-Enhanced visibility graph neural network and its application in anomaly detection
Xu, J., Wang, J., Wu, J., et al. (2026) · doi:10.1109/icnlp69856.2026.11527831
From visibility graphs to cognition
Gautam, S., & Paolo Grigolini, A. (2026) · Frontiers in Network Physiology · doi:10.3389/fnetp.2026.1830261
Higher-order interactions reveal three states of urban-form control over heat-pollution couplingPreprint
Su, W., Huang, C., Dong, G., Xiong, Y., Pei, L., & Yao, J. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.6853612
Rahimi‐Majd, M., Streicher, M., & Nikoloski, Z. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.6854690
Zhang, Z., Lin, C., Xu, X., et al. (2026) · Measurement Science and Technology · doi:10.1088/1361-6501/ae758b
García, C., Pose, F., Campanini, G., et al. (2026) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0318156
Dhebar, J., Das, B., & Rai, A. (2026) · Noise & Vibration Worldwide · doi:10.1177/09574565261459686
Analysis of electric current noise in nano-transistors using visibility graphs
Antoniades, I. P. (2026) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0333518
Network Analysis of Chaotic Dynamics and Stability of Liposomal Nanosystems
Hanias, M. P., Naziris, N., Chountoulesi, M., et al. (2026) · Springer proceedings in complexity · doi:10.1007/978-3-032-09101-7_33
A Novel Crude Oil Price Combination Link Forecasting Method based on the MF-VMD-CDVGNets-SLRNN Model
Zhao, X., Liu, J., Luo, R., et al. (2026) · Cognitive Computation · doi:10.1007/s12559-026-10613-7
Assessing imbalance in signed brain networks
Anonymous, Agrimi, E., Tatullo, S., et al. (2026) · Physical Review Research · doi:10.1103/p6qp-2s9f
PAG: A hybrid graph network for few sample modulation recognition
Feng, H., Guo, Q., Zhou, K., Huang, S., & Tian, Y. (2026) · Digital Signal Processing · doi:10.1016/j.dsp.2026.106360
Multiscale topological analysis of financial markets
Li, C., Xiao-yong, W., Fang, Q., et al. (2026) · International Journal of Modern Physics C · doi:10.1142/s0129183127501117
From ATR-FTIR Spectra to Visibility Graphs: An End-to-End GNN Pipeline for ASD Detection
Araújo, L. G. T., Silva, R. S., & Carneiro, M. G. (2026) · doi:10.5753/sbcas.2026.21273
High-order network analysis for financial crash identification
Бєлінський, А. О., Soloviev, V., Hushko, S. V., Kiv, A. E., & Matviychuk, A. V. (2023) · International Conference on Monitoring, Modeling & Management of Emergent Economy (M3E2) · doi:10.55056/ceur-ws.org/vol-3465/paper15.pdf
An induced complex network-based framework for forecasting chaotic and epidemiological time series
Anjana, S., Nag, S., Kumar, K. S., & Kumar, T. K. M. (2026) · Physics Letters A · doi:10.1016/j.physleta.2026.131952
Analysis of IIoT data using visibility graphs and complex network methods
Xu, J., Wang, K., Wang, J., et al. (2026) · Frontiers in Physics · doi:10.3389/fphy.2026.1864040
Wang, L., & Ma, J.-C. (2026) · Frontiers in Physics · doi:10.3389/fphy.2026.1809470
Balcı, M. A., Akgüller, Ö., Erdoğan, D. R., et al. (2026) · Fractal and Fractional · doi:10.3390/fractalfract10070473
Wu, J., Zhang, X., Li, Z., et al. (2026) · International Journal of Modern Physics C · doi:10.1142/s0129183127501270
Early warning signals for primary and secondary bifurcation to oscillatory instabilities
Radhakrishnan, R., Kumar, P., Pavithran, I., et al. (2026) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0337955
Singh, R., Sane, R., Ranjan, V., Ganguly, A., & Halder, S. (2026) · Physiological Measurement · doi:10.1088/1361-6579/ae8efd
Domínguez-Monterroza, A. (2026) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2026.131896
Radar Signal Recognition Based on DAVG-GRN Network
Tang, Z., Shen, H., & Lam, C. (2026) · Lecture notes in computer science · doi:10.1007/978-981-95-9846-5_12
Qian, L., Fulcher, B., Ju, S., Xiao, Z., Xu, Y., Xia, Y., Zheng, Y., Chen, L., Zou, Y., Schumann, G., et al. (2026) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.64898/2026.08.04.742623
Weighted delayed visibility graph for the analysis of continuous dynamical systems
Yang, G., Zhang, H., Long, D., et al. (2026) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2026.110684
A continuous ordinal patterns-based paradigm for the analysis and comparison of time series
Zanin, M. (2026) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0326702
Hybrid GraphSENet: An efficient hybrid graph network for Speech Emotion Recognition
Sreedutt Ram, J., Poorna, S. S., & Anuraj, K. (2026) · Computers & Electrical Engineering · doi:10.1016/j.compeleceng.2026.111462
Yang, X., & Meng, S. (2026) · Frontiers in Physics · doi:10.3389/fphy.2026.1901452
Olgun, N. (2026) · Scientific Reports · doi:10.1038/s41598-026-68944-2
Complex Network Analysis of Lithium-Ion Battery Life
Singh, M., Pant, S., Chaube, S., Harsh, Kumar, A., & Singh, J. P. (2026) · Prabha Materials Science Letters · doi:10.33889/pmsl.2026.5.2.018
Clustering and imputation of daily water consumption data using visibility algorithms
Acconciaioco, D., Campagnola, M., Enríquez, L., et al. (2026) · Digital Water · doi:10.1080/28375807.2026.2725898
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
