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Related Concept Videos

Graphs of Functions01:30

Graphs of Functions

Graphs of functions provide a visual representation of how output values change in response to varying inputs. Each point on the graph corresponds to an ordered pair, where the x-coordinate (independent variable) determines the horizontal position and the y-coordinate (dependent variable) determines the vertical position. Linear functions like y = x give a straight line, indicating a constant rate of change.Nonlinear functions display more complex behaviors. Even power functions generate...
Graphs of Two-Variable Functions01:27

Graphs of Two-Variable Functions

A weather map provides a practical example of a function of two variables. Across a wide region such as the United States, temperatures vary from one location to another. Each location can be identified by two geographic coordinates: longitude and latitude. Since a single temperature value is assigned to each coordinate pair, the situation can be represented mathematically as a function with two inputs and one output.In mathematical notation, longitude and latitude can be labeled as x and y,...
Graphical Representation of Inequalities01:28

Graphical Representation of Inequalities

The graph of the equation where y equals x squared forms a curve known as a parabola. This curve acts as a boundary in the coordinate plane, dividing it into distinct regions based on the relative position of points.When the equality sign in the equation is replaced with an inequality—such as greater than, less than, greater than or equal to, or less than or equal to—the graphical representation changes from a single curve into a broader shaded area that signifies the set of all points...
Graphs of Equations in Two Variables01:30

Graphs of Equations in Two Variables

An equation with two variables, typically written in the form y = f(x) or Ax + By = C, describes a relationship between quantities represented by x and y. Each solution to such an equation is an ordered pair (x, y) that satisfies the equation when substituted. These pairs can be represented graphically to understand the variables' relationship visually.A common technique for constructing the graph of a two-variable equation is to create a value table. Begin by choosing several values for the...
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
Graphs of Polar Equations01:17

Graphs of Polar Equations

The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...

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Related Experiment Video

Updated: Jun 8, 2026

Recording and Analyzing Multimodal Large-Scale Neuronal Ensemble Dynamics on CMOS-Integrated High-Density Microelectrode Array
09:44

Recording and Analyzing Multimodal Large-Scale Neuronal Ensemble Dynamics on CMOS-Integrated High-Density Microelectrode Array

Published on: March 8, 2024

Greedy connectivity of geographically embedded graphs.

Jie Sun1, Daniel ben-Avraham

  • 1Department of Mathematics & Computer Science, Clarkson University, Potsdam, New York 13699-5815, USA. sunj@clarkson.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
PubMed
Summary

We developed a new metric called greedy connectivity for spatial networks. This measure evaluates how well networks connect using only local information, even with unreliable links, aiding optimal network design.

Related Experiment Videos

Last Updated: Jun 8, 2026

Recording and Analyzing Multimodal Large-Scale Neuronal Ensemble Dynamics on CMOS-Integrated High-Density Microelectrode Array
09:44

Recording and Analyzing Multimodal Large-Scale Neuronal Ensemble Dynamics on CMOS-Integrated High-Density Microelectrode Array

Published on: March 8, 2024

Area of Science:

  • Network Science
  • Graph Theory
  • Spatial Analysis

Background:

  • Geographical networks are crucial for various applications.
  • Designing efficient networks often involves local information and imperfect links.
  • Existing connectivity measures may not fully capture these real-world constraints.

Purpose of the Study:

  • Introduce a novel metric: greedy connectivity for geographical networks.
  • Quantify network performance based on local information and transmission reliability.
  • Provide a criterion for optimizing network design.

Main Methods:

  • Define greedy connectivity for spatial graphs.
  • Incorporate local search strategies for pathfinding.
  • Account for probabilistic link failures and node reachability.

Main Results:

  • Greedy connectivity is larger with higher node reachability probabilities.
  • The metric effectively evaluates networks using local information.
  • Demonstrate the metric's utility in network design scenarios.

Conclusions:

  • Greedy connectivity offers a practical measure for spatial networks.
  • The metric accounts for realistic communication constraints.
  • It serves as a valuable tool for designing robust and efficient networks.