Vector visibility graph from multivariate time series: a new method for characterizing nonlinear dynamic behavior in two-phase flow
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The vector visibility graph (VVG) algorithm extends the univariate visibility graph concept to multivariate time series data.
“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 [25]
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.
“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 [25]
The visibility graph transformation supports both scalar and vector representations, with applications spanning time series analysis and language processing.
“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 [25]
Cites
From time series to complex networks: the visibility graph
Lacasa, L., Luque, B., Ballesteros, F., Luque, J., & Nuño, J. C. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0709247105 · Cited by 1,826 · see citing works
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Emotion Classification With Visibility Graphs
Şimşek, E., Topcu, A., Koç, E., Saritas, E. U., & Koç, A. (2025) · IEEE Signal Processing Letters · doi:10.1109/lsp.2025.3567033 · Cited by 2 · see citing works
- Authors
- Ren, W., & Jin, N.
- Affiliations
- Tianjin University (CN)
- Corresponding author
- Jin, Ningde
- Venue
- Nonlinear Dynamics
- Published
- 2019-07-22
- Volume
- 97
- Issue
- 4
- Pages
- 2547-2556
- ISSN
- 0924-090X (ISSN-L)
- 1573-269X
- OpenAlex
- W2963400705
- Cited by
- 30
- References
- 1
- Citations by year
- 2026: 5 · 2025: 7 · 2024: 1 · 2023: 4 · 2022: 7 · 2021: 3 · 2020: 3
- FWCI
- 4.06
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Nonlinear Dynamics (publishedVersion)
- Funders
- National Natural Science Foundation of China (51527805, 11572220)
- Topics
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Complex Systems and Time Series Analysis
- Physical Sciences › Computer Science › Signal Processing › Time Series Analysis and Forecasting
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
- Keywords
- multivariate time series, directed complex networks, gas-liquid two-phase flow, flow pattern identification, bubbly flow, slug flow, churn flow, degree distribution, scale-free networks, random graphs, fractal time series
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