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Related Concept Videos

Equivalent Resistance01:16

Equivalent Resistance

In circuit analysis, situations often arise where resistors are neither in series nor parallel configurations. To tackle such scenarios, three-terminal equivalent networks like the wye (Y) (Figure 1 (a)) or tee (T) and delta (Δ) (Figure 1 (b)) or pi (π) networks come into play. These networks offer versatile solutions and are frequently encountered in various applications, including three-phase electrical systems, electrical filters, and matching networks.
Odds Ratio01:09

Odds Ratio

The odds ratio (OR) is a statistical measure used extensively in epidemiology and research to quantify the strength of association between exposure and outcome across different groups. Unlike relative risk, which compares the probabilities of an event occurring, the odds ratio compares the odds of an event occurring in the exposed group to the odds of it occurring in the unexposed group. The odds, in this context, are calculated as the probability of the event happening divided by the...
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...
Relative Risk01:12

Relative Risk

Relative risk (RR) is a statistical measure commonly used in epidemiology to compare the likelihood of a particular event occurring between two groups. This metric is important for evaluating the relationship between exposure to a specific risk factor and the probability of a particular outcome. It plays a crucial role in medical research, public health studies, and risk assessment. Relative risk quantifies how much more (or less) likely an event is to occur in an exposed group compared to an...
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first column of the Routh...
Relationship Formation02:12

Relationship Formation

What do you think is the single most influential factor in determining with whom you become friends and whom you form romantic relationships? You might be surprised to learn that the answer is simple: the people with whom you have the most contact. This most important factor is proximity. You are more likely to be friends with people you have regular contact with. For example, there are decades of research that shows that you are more likely to become friends with people who live in your dorm,...

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Related Experiment Video

Updated: Jun 14, 2026

Divergence of Root Microbiota in Different Habitats based on Weighted Correlation Networks
09:49

Divergence of Root Microbiota in Different Habitats based on Weighted Correlation Networks

Published on: September 25, 2021

Edge ratio and community structure in networks.

Sonia Cafieri1, Pierre Hansen, Leo Liberti

  • 1LIX, Ecole Polytechnique, F-91128 Palaiseau, France. cafieri@lix.polytechnique.fr

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 7, 2010
PubMed
Summary

A new hierarchical divisive algorithm identifies communities in complex networks by optimizing edge ratios. This method proves competitive with modularity maximization and offers valuable insights into network structures.

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Last Updated: Jun 14, 2026

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Area of Science:

  • Network Science
  • Computer Science
  • Data Mining

Background:

  • Identifying community structures is crucial for understanding complex networks.
  • Existing methods like modularity maximization have limitations in certain network scenarios.
  • The definition of community in the weak sense provides a basis for optimization.

Purpose of the Study:

  • To propose a novel hierarchical divisive algorithm for community detection in complex networks.
  • To extend the weak community definition into an optimality criterion for bipartitioning.
  • To compare the performance of the new algorithm against exact modularity maximization.

Main Methods:

  • Developed a hierarchical divisive algorithm based on optimizing the ratio of inner to cut edges.
  • Utilized a mathematical program within a dichotomous search for optimal bipartitioning.
  • Included an exact solution for detecting indivisible communities.

Main Results:

  • The proposed edge ratio algorithm found optimal solutions for artificial network problems.
  • It demonstrated competitiveness with modularity maximization on real-world datasets.
  • The algorithm provided additional information, particularly through dendrogram visualization.

Conclusions:

  • The hierarchical divisive algorithm is an effective method for community detection.
  • It offers a competitive alternative to modularity maximization, especially when visualizing resolution.
  • The algorithm shows comparable results to established methods on benchmark datasets.