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Related Concept Videos

Ogive Graph01:07

Ogive Graph

An ogive graph is sometimes called a cumulative frequency polygon. It is one type of frequency polygon that shows cumulative frequency. In other words, the cumulative percentages are added to the graph from left to right. An ogive graph plots cumulative frequency on the vertical y-axis and class boundaries along the horizontal x-axis. It’s very similar to a histogram; only instead of rectangles, an ogive displays a single point where the top right of the rectangle would be. Creating this type...
Time-Series Graph00:54

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...
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Velocity and Position by Graphical Method

Velocity and position can be calculated from the known function of acceleration as a function of time. The total area under the acceleration-time graph and the velocity-time graph gives the change in velocity and position, respectively. In the case of an airplane, its acceleration is tracked using the inertial navigation system. The pilot provides the input of the airplane's initial position and velocity before takeoff. The inertial navigation system then uses the acceleration data to calculate...
Bar Graph01:07

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...
Pareto Chart00:52

Pareto Chart

A Pareto chart is a bar graph or a combination of both line and bar graphs. The bar lengths represent the individual values or the frequency, while the lines represent the cumulative total values. In this chart, the longest bars are arranged on the left and the shortest bars on the right, which makes it easier to read and interpret the data. It can also be called a Pareto diagram or Pareto analysis.
The Pareto chart is named after the Italian economist Vilfredo Pareto, who described the Pareto...
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Outliers and Influential Points

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Related Experiment Video

Updated: Jul 23, 2026

Studying Cell Rolling Trajectories on Asymmetric Receptor Patterns
04:24

Studying Cell Rolling Trajectories on Asymmetric Receptor Patterns

Published on: February 13, 2011

On the edges' PageRank and line graphs.

Regino Criado1, Santiago Moral1, Ángel Pérez1

  • 1Department of Applied Mathematics, Rey Juan Carlos University, 28933 Madrid, Spain.

Chaos (Woodbury, N.Y.)
|August 3, 2018
PubMed
Summary

This study introduces two methods for calculating edge PageRank in directed networks, finding them equivalent. One method offers significant computational benefits for network analysis applications.

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Area of Science:

  • Network Science
  • Graph Theory
  • Computer Science

Background:

  • PageRank is a well-established algorithm for ranking nodes in networks.
  • Defining PageRank for edges in directed networks is an emerging area of research.
  • Applications span cybersecurity and transportation systems.

Purpose of the Study:

  • To define and compare two distinct approaches for calculating edge PageRank in directed, possibly weighted networks.
  • To demonstrate the equivalence of these two approaches.
  • To highlight the practical utility of edge PageRank through real-world examples.

Main Methods:

  • Development of two novel methodologies for edge PageRank computation.
  • Theoretical analysis to prove the equivalence of the proposed methods.
  • Application of edge PageRank to cybersecurity threat detection and subway network analysis.

Main Results:

  • Demonstrated mathematical equivalence between the two proposed edge PageRank calculation methods.
  • Identified one approach with superior computational efficiency.
  • Validated the practical applicability of edge PageRank in cybersecurity and transportation network simulations.

Conclusions:

  • The proposed edge PageRank methods provide a robust framework for analyzing network structure and importance.
  • The computationally advantageous method facilitates scalable analysis of large-scale networks.
  • Edge PageRank offers valuable insights for applications in cybersecurity and urban transit systems.