# Horizontal visibility graphs transformed from fractional Brownian motions: Topological properties versus the Hurst index

@article{Xie2011HorizontalVG, title={Horizontal visibility graphs transformed from fractional Brownian motions: Topological properties versus the Hurst index}, author={Wen-Jie Xie and Wei‐Xing Zhou}, journal={Physica A-statistical Mechanics and Its Applications}, year={2011}, volume={390}, pages={3592-3601} }

## 54 Citations

### Multifractality and Laplace spectrum of horizontal visibility graphs constructed from fractional Brownian motions

- Mathematics
- 2016

Many studies have shown that additional information can be gained on time series by investigating their associated complex networks. In this work, we investigate the multifractal property and Laplace…

### Topological properties and fractal analysis of a recurrence network constructed from fractional Brownian motions.

- Mathematics, Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2014

The results strongly suggest that the recurrence network inherits the basic characteristic and the fractal nature of the associated FBM series.

### Time series characterization via horizontal visibility graph and Information Theory

- Computer Science
- 2016

### Fractal analysis of recurrence networks constructed from the two-dimensional fractional Brownian motions.

- MathematicsChaos
- 2020

In this study, we focus on the fractal property of recurrence networks constructed from the two-dimensional fractional Brownian motion (2D fBm), i.e., the inter-system recurrence network, the joint…

### Time irreversibility and intrinsics revealing of series with complex network approach

- Computer SciencePhysica A: Statistical Mechanics and its Applications
- 2018

### Horizontal visibility graphs from integer sequences

- Mathematics
- 2016

The horizontal visibility graph (HVG) is a graph-theoretical representation of a time series and builds a bridge between dynamical systems and graph theory. In recent years this representation has…

### Network analysis of time series under the constraint of fixed nearest neighbors

- Computer Science, Mathematics
- 2013

### Persistent homology of fractional Gaussian noise.

- MathematicsPhysical review. E
- 2021

The persistence entropy logarithmically grows with the size of the visibility graph of a system with almost H-dependent prefactors, and the correlated behavior of electroencephalography for both healthy and schizophrenic samples is shown.

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Fractional Brownian motion (fBm) has been used as a theoretical framework to study real-time series appearing in diverse scientific fields. Because of its intrinsic nonstationarity and long-range…

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The horizontal visibility algorithm is used to characterize and distinguish between correlated stochastic, uncorrelated and chaotic processes, and it is shown that in every case the series maps into a graph with exponential degree distribution P(k)∼exp(-λk), where the value of λ characterizes the specific process.

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This work presents the horizontal visibility algorithm, a geometrically simpler and analytically solvable version of the former algorithm, focusing on the mapping of random series (series of independent identically distributed random variables), and presents exact results on the topological properties of graphs associated with random series, namely, the degree distribution, the clustering coefficient, and the mean path length.

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This work investigates 30 world stock market indices through their visibility graphs by adopting the visibility algorithm to convert each single stock index into one visibility graph, finding a universal allometric scaling law is uncovered in the minimal spanning trees and the random spanning trees.

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A simple and fast computational method, the visibility algorithm, that converts a time series into a graph, which inherits several properties of the series in its structure, enhancing the fact that power law degree distributions are related to fractality.

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The superfamily phenomenon of time series with different dynamics can be characterized by the motif-rank patterns observed in the nearest-neighbor networks of the time series in phase space. However,…