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Time-Series Graph

Time-Series Graph

A time-series graph is a line graph with repeated measurements taken at successive intervals of time. It is also called a time series chart. To construct a time-series graph, one must look at both pieces of a paired data set. The horizontal axis is used to plot the time increments, and the vertical axis is used to plot the values of the variable that one is measuring. By using the axes in this way, each point on the graph will correspond to time and a measured quantity. The points on the graph...

Relative Frequency Histogram

Relative Frequency Histogram

The relative frequency depicts the proportion of data points that have each value. The frequency tells the number of data points that have each value. Like the histogram, a relative frequency histogram also has the same shape with a horizontal scale (the x-axis), but the vertical scale (the y-axis) is marked with relative frequencies (percentages of the whole) instead of actual frequencies. A relative frequency histogram is a graphical representation of a frequency distribution where the...

Multiple Bar Graph

Multiple Bar Graph

As the name suggests, a multiple bar graph is the same as a bar graph but has multiple bars to depict relationships between different data values. One can include as many parameters as possible. However, each parameter must have the same unit of measurement.
Each bar or column in the multiple bar graph represents a data value. These graphs are used primarily in interrelating two or more sets of data. The categories of different kinds of data are listed along the horizontal or x-axis, whereas...

Probability Histograms

Probability Histograms

A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.

Bar Graph

Bar Graph

A bar graph is also called a bar chart and consists of bars that are separated from each other. It either uses horizontal or vertical bars to show comparisons among categories. The bars can be rectangles, or they can be rectangular boxes (used in three-dimensional plots). One axis of the graph represents the specific categories being compared, and the other axis shows a discrete value. In this graph, the length of the bar for each category is proportional to the number or percent of individuals...

Histogram

Histogram

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Related Experiment Video

Updated: Jun 18, 2026

Evaluating Usability Aspects of a Mixed Reality Solution for Immersive Analytics in Industry 4.0 Scenarios

Evaluating Usability Aspects of a Mixed Reality Solution for Immersive Analytics in Industry 4.0 Scenarios

Published on: October 6, 2020

Horizontal visibility graphs: exact results for random time series.

B Luque¹, L Lacasa, F Ballesteros

¹Departamento Matemática Aplicada y Estadística, ETSI Aeronáuticos, Universidad Politécnica de Madrid, Madrid, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|November 13, 2009

Summary

The horizontal visibility algorithm maps time series to complex networks, effectively distinguishing random series from non-random and chaotic ones. This method provides a simple yet powerful tool for time series analysis and characterization.

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Area of Science:

Complex network theory
Time series analysis
Statistical physics

Background:

The visibility algorithm maps time series to complex networks, enabling the application of network theory methods.
A simpler, analytically solvable version, the horizontal visibility algorithm, is introduced for random series analysis.

Purpose of the Study:

To present the horizontal visibility algorithm and its properties.
To derive exact results for the topological properties of graphs generated from random series.
To demonstrate the algorithm's ability to differentiate chaotic from random time series.

Main Methods:

Mapping time series to complex networks using the horizontal visibility algorithm.
Analyzing topological properties: degree distribution, clustering coefficient, mean path length.
Applying the algorithm to noise-free and noisy chaotic series, including high-dimensional systems.

Main Results:

Random series map to graphs with a specific exponential degree distribution: P(k)=(1/3)(2/3)(k-2).
Deviations from this distribution indicate non-random series.
The algorithm successfully distinguishes chaotic series from i.i.d. series, even with significant noise.

Conclusions:

The horizontal visibility algorithm is a robust method for identifying randomness in time series.
It serves as a powerful tool for distinguishing chaotic dynamics without preprocessing.
The method's effectiveness is confirmed by theoretical results and numerical simulations.