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 801–900 of 1,826
Discriminating Chaotic Time Series with Visibility Graph Eigenvalues
Fioriti, V. A., Tofani, A., Pietro, A. D., et al. (2012) · Complex Systems · doi:10.25088/complexsystems.21.3.193 · Cited by 9
Mondal, S., Bhattacharya, C., Chattopadhyay, P., et al. (2017) · AIAA/SAE/ASEE Joint Propulsion Conference (JPC) · doi:10.2514/6.2017-4892 · Cited by 9
Network topology of turbulent premixed Bunsen flame at elevated pressure and turbulence intensity
Wang, J., Nie, Y., Zhang, W., Guo, S., Zhang, M., & Huang, Z. (2019) · Aerospace Science and Technology · doi:10.1016/j.ast.2019.105361 · Cited by 9
Device-Free Orientation Detection Based on CSI and Visibility Graph
Wu, Z., Pan, X., Fan, K., et al. (2019) · IEEE Transactions on Systems Man and Cybernetics Systems · doi:10.1109/tsmc.2019.2933161 · Cited by 9
Multiscale horizontal visibility entropy: Measuring the temporal complexity of financial time series
Zhao, X., & Zhang, P. (2019) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2019.122674 · Cited by 9
A preliminary study on atrial epicardial mapping signals based on Graph Theory
Sun, L., Yang, C., Zhang, L., et al. (2014) · Medical Engineering & Physics · doi:10.1016/j.medengphy.2014.03.011 · Cited by 9
A Patient Suffering From Neurodegenerative Disease May Have a Strengthened Fractal Gait Rhythm
Ren, H., Yang, Y., Gu, C., Weng, T., & Yang, H. (2018) · IEEE Transactions on Neural Systems and Rehabilitation Engineering · doi:10.1109/tnsre.2018.2860971 · Cited by 9
Lee, S., Choi, J., & Son, Y. (2023) · Annals of Operations Research · doi:10.1007/s10479-022-05071-x · Cited by 8
Sharma, N., & Joshi, D. (2025) · IEEE Transactions on Consumer Electronics · doi:10.1109/tce.2025.3540875 · Cited by 8
Mishra, A., Dhebar, J., & Rai, A. (2025) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2025.113250 · Cited by 8
Lv, Y., Liu, H., Yuan, R., Dong, X., Wang, Y., Wu, H., & Chelidze, D. (2026) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2026.113919 · Cited by 10
Persistent homology of coarse-grained state-space networks
Myers, A., Chumley, M. M., Khasawneh, F. A., et al. (2023) · Physical review. E · doi:10.1103/physreve.107.034303 · Cited by 8
Mapping time series into signed networks via horizontal visibility graph
Gao, M., & Ge, R. (2023) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2023.129404 · Cited by 8
Photoplethysmography-based cuffless blood pressure estimation: an image encoding and fusion approach
Liu, Y., Yu, J., & Mou, H. (2023) · Physiological Measurement · doi:10.1088/1361-6579/ad0426 · Cited by 8
Zhu, M., Xu, H., Wang, M., et al. (2024) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2024.129543 · Cited by 8
Angelidis, A. K., Goulas, K., Bratsas, C., et al. (2024) · Entropy · doi:10.3390/e26040341 · Cited by 8
Khan, W. H., Khan, M. S., Khan, N., Ahmad, A., Siddiqui, Z. I., Singh, R. K., & Malik, M. Z. (2024) · Elsevier eBooks · doi:10.1016/b978-0-443-21870-5.00006-6 · Cited by 8
Zanin, M., & Papo, D. (2025) · Entropy · doi:10.3390/e27020126 · Cited by 8
Natural visibility graphs for diagnosing attention deficit hyperactivity disorder (ADHD)
Mira‐Iglesias, A., Conejero, J. A., & Navarro‐Pardo, E. (2016) · Electronic Notes in Discrete Mathematics · doi:10.1016/j.endm.2016.09.058 · Cited by 8
Olamat, A., Shams, P., & Akan, A. (2017) · Medical Technologies National Congress (TIPTEKNO) · doi:10.1109/tiptekno.2017.8238041 · Cited by 8
Universal law in the crude oil market based on visibility graph algorithm and network structure
Wang, F., Tian, L., Du, R., et al. (2021) · Resources Policy · doi:10.1016/j.resourpol.2020.101961 · Cited by 8
Matching Intensity for Image Visibility Graphs: A New Method to Extract Image Features
Zhu, D., Semba, S., & Yang, H. (2021) · IEEE Access · doi:10.1109/access.2021.3050747 · Cited by 8
A novel prediction model of multi-layer symbolic pattern network: Based on causation entropy
Wang, X., & Sun, M. (2021) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2021.126045 · Cited by 8
Zervou, M. A., Doutsi, E., Pavlidis, P., & Tsakalides, P. (2021) · Bioinformatics · doi:10.1093/bioinformatics/btab407 · Cited by 8
Xu, H., & Wang, M. (2021) · Complexity · doi:10.1155/2021/3052041 · Cited by 8
Cuff-Less Blood Pressure Estimation via Small Convolutional Neural Networks
Wang, W., Mohseni, P., Kilgore, K., & Najafizadeh, L. (2021) · Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) · doi:10.1109/embc46164.2021.9630557 · Cited by 8
Wang, F., Wang, L., & Chen, Y. (2022) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2022.111893 · Cited by 8
Telesca, L., Thai, A. T., Lovallo, M., et al. (2022) · Entropy · doi:10.3390/e24111620 · Cited by 8
Dynamic Phase and Group Detection in Pedestrian Crowd Data Using Multiplex Visibility Graphs
Stephen, C. (2015) · Procedia Computer Science · doi:10.1016/j.procs.2015.07.318 · Cited by 8
Visitor flow pattern of Expo 2010
Fan, C., & Guo, J.-L. (2012) · Chinese Physics B · doi:10.1088/1674-1056/21/7/070209 · Cited by 8
Tumor Growth in the Brain: Complexity and Fractality
Martı́n-Landrove, M., Brú, A., Rueda-Toicen, A., et al. (2016) · Springer series in computational neuroscience · doi:10.1007/978-1-4939-3995-4_22 · Cited by 8
Estimation of Dynamic Bivariate Correlation Using a Weighted Graph Algorithm
John, M., Wu, Y., Narayan, M., John, A., Ikuta, T., & Ferbinteanu, J. (2020) · Entropy · doi:10.3390/e22060617 · Cited by 8
Transformation from Graphs to Signals and Back
Hamon, R., Borgnat, P., Flandrin, P., et al. (2018) · Signals and communication technology · doi:10.1007/978-3-030-03574-7_2 · Cited by 8
Time series classification based on triadic time series motifs
Xie, W.-J., Han, R.-Q., & Zhou, W.-X. (2019) · International Journal of Modern Physics B · doi:10.1142/s0217979219502370 · Cited by 8
A New Recurrence-Network-Based Time Series Analysis Approach for Characterizing System Dynamics
Yang, G., Xu, D., & Zhang, H. (2019) · Entropy · doi:10.3390/e21010045 · Cited by 8
Network community detection from the perspective of time series
Wang, D., & Zhao, Y. (2019) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2019.01.028 · Cited by 8
Methods of Nonlinear Time Series Analysis and Applications: A Review
Ambika, G., & Harikrishnan, K. P. (2019) · Energy, environment, and sustainability · doi:10.1007/978-981-15-0536-2_2 · Cited by 8
Three-level network analysis of the North American natural gas price: A multiscale perspective
Liu, S., Huang, S., Chi, Y., et al. (2019) · International Review of Financial Analysis · doi:10.1016/j.irfa.2019.101420 · Cited by 8
Telesca, L., Chen, C.-C., & Lovallo, M. (2020) · Pure and Applied Geophysics · doi:10.1007/s00024-020-02470-8 · Cited by 8
Creating Directed Weighted Network of Terms Based on Analysis of Text Corpora
Lande, D., & Dmytrenko, O. (2020) · IEEE International Conference on System Analysis & Intelligent Computing (SAIC) · doi:10.1109/saic51296.2020.9239182 · Cited by 8
Planar visibility graph network algorithm for two dimensional timeseries
Liu, J., & Li, Q. (2017) · Chinese Control and Decision Conference (CCDC) · doi:10.1109/ccdc.2017.7978727 · Cited by 8
Causality structures in nonlinear dynamical systems
Wan, H., Wang, H., Gu, C., et al. (2024) · Nonlinear Dynamics · doi:10.1007/s11071-024-10700-0 · Cited by 7
Identifying Influential Nodes Based on Evidence Theory in Complex Network
Tan, F., Chen, X., Chen, R., et al. (2025) · Entropy · doi:10.3390/e27040406 · Cited by 7
Minimising Entropy Changes in Dynamic Network Evolution
Wang, J., Wilson, R. C., & Hancock, E. R. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-58961-9_23 · Cited by 7
Directed Graph Evolution from Euler-Lagrange Dynamics
Wang, J., Wilson, R. C., & Hancock, E. R. (2018) · Proceedings - International Conference on Pattern Recognition/Proceedings/International Conference on Pattern Recognition · doi:10.1109/icpr.2018.8546316 · Cited by 7
Time series pattern identification by hierarchical community detection
Anghinoni, L., Vega‐Oliveros, D. A., Silva, T. C., et al. (2021) · The European Physical Journal Special Topics · doi:10.1140/epjs/s11734-021-00163-4 · Cited by 7
Wang, F., & Zhang, Z. (2022) · Atmosphere · doi:10.3390/atmos14010055 · Cited by 7
A simple scalable linear time algorithm for horizontal visibility graphs
Schmidt, J., & Köhne, D. (2023) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2023.128601 · Cited by 7
Bai, H., Yang, J., Huang, M., et al. (2023) · IET Communications · doi:10.1049/cmu2.12608 · Cited by 7
Shahriari, Z., Algar, S. D., Walker, D. M., et al. (2023) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0141438 · Cited by 7
Visibility graph and graph convolution networks-based segmentation of carbon emission in China
Hu, J., Chu, C., Criado, R., et al. (2023) · Annals of Operations Research · doi:10.1007/s10479-023-05623-9 · Cited by 7
Chen, L., Zhang, X., Li, Z., et al. (2024) · Sensors · doi:10.3390/s24103234 · Cited by 7
Forecasting Turning Points in Stock Price by Integrating Chart Similarity and Multipersistence
Li, S., Liu, Y., Chen, X., Wu, J., & Xu, K. (2024) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2024.3444814 · Cited by 8
Wu, C., Zhang, L., Tang, Z., Dong, X., & Hua, H. (2024) · IEEE Sensors Journal · doi:10.1109/jsen.2024.3492038 · Cited by 7
DTSG-Net: Dynamic Time Series Graph Neural Network and Its Application in Modulation Recognition
Yin, P., Zhou, J., Ge, Y., et al. (2024) · IEEE Internet of Things Journal · doi:10.1109/jiot.2024.3514875 · Cited by 7
Flores-Cadena, M., Matamoros, O. M., Padilla, R. T., et al. (2011) · Fractals · doi:10.1142/s0218348x11005488 · Cited by 7
Directed network topologies of smart grain sensors
Walker, D. M., Tordesillas, A., Nakamura, T., et al. (2013) · Physical Review E · doi:10.1103/physreve.87.032203 · Cited by 7
Wang, X.-X., Xu, L., Yu, J., et al. (2019) · Advanced Engineering Informatics · doi:10.1016/j.aei.2019.100957 · Cited by 7
Chinese cities’ air quality pattern and correlation
Zhang, W., Guan, Z., Li, J., et al. (2020) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/ab7813 · Cited by 7
Nault, S., Creuze, V., Al-Omar, S., et al. (2020) · Frontiers in Physiology · doi:10.3389/fphys.2020.00585 · Cited by 7
Choudhary, G. I., Aziz, W., & Fränti, P. (2020) · Biomedical Signal Processing and Control · doi:10.1016/j.bspc.2020.102052 · Cited by 7
Nonlinear Correlation Analysis of Time Series Based on Complex Network Similarity
Nie, C.-X. (2020) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127420502259 · Cited by 7
Complex network perspective on modelling chaotic systems via machine learning*
Weng, T., Cao, X., & Yang, H. (2021) · Chinese Physics B · doi:10.1088/1674-1056/abd9b3 · Cited by 8
Random-Walk Laplacian for Frequency Analysis in Periodic Graphs
Boukrab, R., & Pagés-Zamora, A. (2021) · Sensors · doi:10.3390/s21041275 · Cited by 7
Testing for nonlinearity in nonstationary time series: A network-based surrogate data test
Mallika, M., Prabhaa, S. S., Asokan, K., et al. (2021) · Physical review. E · doi:10.1103/physreve.104.054217 · Cited by 7
Intelligent algorithm for dynamic functional brain network complexity from CN to AD
Zhang, C., Cui, X., Lian, S., Xiao, R., Qiao, H., Li, S., Lou, Y., Feng, Y., Zhuang, L., Du, J., et al. (2021) · International Journal of Intelligent Systems · doi:10.1002/int.22737 · Cited by 7
Ma, Z., Yang, X., He, A., et al. (2022) · Acta Physica Sinica · doi:10.7498/aps.71.20211656 · Cited by 7
Transformation cost spectrum for irregularly sampled time series
Ozdes, C., & Eroglu, D. (2022) · The European Physical Journal Special Topics · doi:10.1140/epjs/s11734-022-00512-x · Cited by 7
Cai, Q., An, J.-P., Li, H., Guo, J., & Gao, Z. (2022) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0098454 · Cited by 7
Zare, M., & Nouri, N. M. (2022) · Ocean Engineering · doi:10.1016/j.oceaneng.2022.112700 · Cited by 7
A linear time series analysis of carbon price via a complex network approach
Hu, Y., Chu, C., Wu, P. C., & Hu, J. (2022) · Frontiers in Physics · doi:10.3389/fphy.2022.1029600 · Cited by 7
Aranburu‐Imatz, A., Jiménez‐Hornero, J. E., Morales‐Cané, I., et al. (2023) · Air Quality Atmosphere & Health · doi:10.1007/s11869-023-01310-7 · Cited by 7
From time series to networks in R with the ts2net package
Ferreira, L. N. (2024) · Applied Network Science · doi:10.1007/s41109-024-00642-2 · Cited by 7
EVOLUTIONARY GAMES ON VISIBILITY GRAPHS
Bašič, A. M., & Perc, M. (2011) · Advances in Complex Systems · doi:10.1142/s0219525911002974 · Cited by 7
Deep Co-Investment Network Learning for Financial Assets
Wang, Y., Zhang, C., Wang, S., Yu, P. S., Bai, L., & Cui, L. (2018) · IEEE International Conference on Big Knowledge (ICBK) · doi:10.1109/icbk.2018.00014 · Cited by 10
An Improved Visibility Graph Analysis of EEG Signals of Alzheimer Brain
Wang, R., Yang, Z., Wang, J., et al. (2018) · International Congress on Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI) · doi:10.1109/cisp-bmei.2018.8633052 · Cited by 7
Xu, H., Wang, M., & Yang, W. (2019) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2019.03.067 · Cited by 7
Feature Selection Using Ant Colony Optimization and Weighted Visibility Graph
Sekhar, L. C., & Vijayakumar, R. (2020) · Advances in intelligent systems and computing · doi:10.1007/978-981-15-5788-0_3 · Cited by 7
Analysis of Stock Price Motion Asymmetry via Visibility-Graph Algorithm
Liu, R., & Chen, Y. (2020) · Frontiers in Physics · doi:10.3389/fphy.2020.539521 · Cited by 7
An electrostatics method for converting a time-series into a weighted complex network
Tsiotas, D., Magafas, L., & Argyrakis, P. (2021) · Scientific Reports · doi:10.1038/s41598-021-89552-2 · Cited by 7
Change-point detection with recurrence networks
Iwayama, K., Hirata, Y., Suzuki, H., et al. (2013) · Nonlinear Theory and Its Applications IEICE · doi:10.1587/nolta.4.160 · Cited by 7
Hao, C., Li, W., & Du, S. (2016) · IEEE International Conference on Cyber Technology in Automation, Control, and Intelligent Systems · doi:10.1109/cyber.2016.7574867 · Cited by 7
Murari, A., Craciunescu, T., Peluso, E., et al. (2017) · Entropy · doi:10.3390/e19100569 · Cited by 7
Network stiffness: A new topological property in complex networks
Tsiotas, D. (2019) · PLoS ONE · doi:10.1371/journal.pone.0218477 · Cited by 7
Bigon, L., Cassani, G., Greco, C., et al. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1907.00400 · Cited by 7
Self-citationМережні міри складності соціально-економічних систем
Соловйов, В. М. (2015) · doi:10.31812/0564/1158 · Cited by 7
Speaker diarization and tracking in multiple-sensor environments
Serrano, J. L. (2012) · doi:10.5821/dissertation-2117-94956 · Cited by 7
Hurst exponent estimation using natural visibility graph embedding in Fisher–Shannon plane
Averty, T., Boudraa, A., & Daré-Emzivat, D. (2025) · Signal Processing · doi:10.1016/j.sigpro.2024.109884 · Cited by 6
Vontzos, G., Laitsos, V. M., Bargiotas, D., Fevgas, A., Daskalopulu, A., & Tsoukalas, L. H. (2025) · Electricity · doi:10.3390/electricity6020017 · Cited by 6
Yaser, S., Chowdhury, M. E. H., & Sarmun, R. (2025) · Computers in Biology and Medicine · doi:10.1016/j.compbiomed.2025.110536 · Cited by 6
Sea-Surface Small Floating Targets Detection Based on Graph Smoothing Characteristics
Ru, H., Xu, S., He, Q., et al. (2025) · IEEE Transactions on Aerospace and Electronic Systems · doi:10.1109/taes.2025.3590357 · Cited by 6
Anuraj, K., & Menon, V. (2025) · IEEE Sensors Journal · doi:10.1109/jsen.2025.3618310 · Cited by 6
Rodríguez, M. A. (2016) · Physical review. E · doi:10.1103/physreve.94.012314 · Cited by 6
Zhang, Y., & Wang, J. (2017) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2017.04.166 · Cited by 6
Wang, Z., Shang, P., & Shang, B. (2022) · Communications in Nonlinear Science and Numerical Simulation · doi:10.1016/j.cnsns.2022.106985 · Cited by 6
Ramezanpoor, Z., Ghazikhani, A., & Bajestani, G. S. (2023) · Engineering Applications of Artificial Intelligence · doi:10.1016/j.engappai.2023.107557 · Cited by 6
Caö, H., & Li, Y. (2024) · Mathematics · doi:10.3390/math12020204 · Cited by 6
Hard c-means transition network for the analysis of multivariate time series
Yang, G., Long, D., Wang, K., et al. (2024) · Nonlinear Dynamics · doi:10.1007/s11071-024-09523-w · Cited by 6
LAC: A Workload Intensity-Aware Caching Scheme for High-Performance SSDs
Sun, H., Tong, H., Yue, Y., et al. (2024) · IEEE Transactions on Computers · doi:10.1109/tc.2024.3385290 · Cited by 6
Characteristics of Air Traffic Flow in Terminal Airspace: A Multiplex Recurrence Network Analysis
Jiang, F., & Zhang, Z. (2024) · IEEE Transactions on Intelligent Transportation Systems · doi:10.1109/tits.2024.3396627 · Cited by 6
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
