Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Graphical Representation of Inequalities01:28

Graphical Representation of Inequalities

424
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...
424
Equity Theory01:26

Equity Theory

408
Equity theory explains how our sense of fairness influences the dynamics of close relationships. Rooted in social psychology, the theory posits that individuals evaluate fairness by comparing the ratio of their contributions to the rewards they receive. Relationship satisfaction is highest when these ratios are perceived as balanced between partners, promoting mutual reciprocity and a sense of justice.Equity vs. Equality in RelationshipsEquity is distinct from equality. Fairness does not...
408
Randomized Experiments01:13

Randomized Experiments

9.4K
The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally assigned. Randomization is meant to eliminate selection bias and balance known and unknown confounding factors so that the control group is similar to the treatment group as much as possible. A computer program and a random number generator can be used to assign participants to groups in a way that minimizes bias.
Simple randomization
Simple...
9.4K
Random Variables01:09

Random Variables

19.3K
A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
19.3K
Probability Distributions01:32

Probability Distributions

13.7K
 The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
13.7K
Graphs of Equations in Two Variables01:30

Graphs of Equations in Two Variables

401
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...
401

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Mutual information and the encoding of contingency tables.

Physical review. E·2025
Same author

Luck, skill, and depth of competition in games and social hierarchies.

Science advances·2024
Same author

Hierarchical core-periphery structure in networks.

Physical review. E·2023
Same author

Clustering of heterogeneous populations of networks.

Physical review. E·2022
Same author

Reconstruction of plant-pollinator networks from observational data.

Nature communications·2021
Same author

Belief propagation for networks with loops.

Science advances·2021
Same journal

Tension on dsDNA bound to ssDNA-RecA filaments may play an important role in driving efficient and accurate homology recognition and strand exchange.

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Amplitude-phase coupling drives chimera states in globally coupled laser networks [Phys. Rev. E 91, 040901(R) (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Attenuation of excitation decay rate due to collective effect [Phys. Rev. E 90, 022142 (2014)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells [Phys. Rev. E 92, 052715 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Lattice Boltzmann approach for complex nonequilibrium flows [Phys. Rev. E 92, 043308 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
See all related articles

Related Experiment Video

Updated: Apr 19, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

1.2K

Equitable random graphs.

M E J Newman1, Travis Martin2

  • 1Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48109, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2014
PubMed
Summary
This summary is machine-generated.

Equitable random graphs offer a flexible framework for modeling complex networks. These models allow for diverse structures and degree distributions, while remaining exactly solvable for key properties.

More Related Videos

Soft Pneumatic Robot Modulates Graph Theory Metrics of Brain Network for Hand Rehabilitation After Stroke
05:30

Soft Pneumatic Robot Modulates Graph Theory Metrics of Brain Network for Hand Rehabilitation After Stroke

Published on: October 10, 2025

656
The HoneyComb Paradigm for Research on Collective Human Behavior
06:48

The HoneyComb Paradigm for Research on Collective Human Behavior

Published on: January 19, 2019

10.0K

Related Experiment Videos

Last Updated: Apr 19, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

1.2K
Soft Pneumatic Robot Modulates Graph Theory Metrics of Brain Network for Hand Rehabilitation After Stroke
05:30

Soft Pneumatic Robot Modulates Graph Theory Metrics of Brain Network for Hand Rehabilitation After Stroke

Published on: October 10, 2025

656
The HoneyComb Paradigm for Research on Collective Human Behavior
06:48

The HoneyComb Paradigm for Research on Collective Human Behavior

Published on: January 19, 2019

10.0K

Area of Science:

  • Network Science
  • Graph Theory
  • Statistical Physics

Background:

  • Random graph models like Erdős-Rényi and configuration models are foundational in network analysis.
  • Existing models often struggle to capture complex network structures and diverse degree distributions.

Purpose of the Study:

  • Introduce a new class of random graph models: equitable random graphs.
  • Demonstrate the flexibility of equitable random graphs in representing diverse network structures.
  • Highlight the analytical tractability of equitable random graphs for various network properties.

Main Methods:

  • Develop the mathematical framework for equitable random graph generation.
  • Analyze the properties of equitable random graphs in the large graph size limit.
  • Investigate the solvability of key network characteristics within this model.

Main Results:

  • Equitable random graphs can represent diverse structures like community and bipartite structures.
  • These models accommodate varied degree distributions and degree correlations.
  • Exact solutions are obtainable for percolation, spectral density, and dynamical systems.

Conclusions:

  • Equitable random graphs provide a powerful and versatile tool for theoretical network analysis.
  • The exact solvability of these models facilitates deeper understanding of complex networked systems.
  • This framework extends the applicability of random graph theory to more realistic network scenarios.