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Related Concept Videos

Symmetry01:26

Symmetry

The equation of an ellipse centered at the origin defines all points whose distances from the center maintain a constant ratio between the horizontal and vertical axes. This equation results in a smooth, closed curve that extends further along the x-axis than the y-axis, giving it a horizontal orientation. Such an ellipse demonstrates three kinds of symmetry: across the x-axis, across the y-axis, and about the origin. These symmetries are essential in understanding the graph's structure and...
Even and Odd Signals01:17

Even and Odd Signals

An even signal, whether in continuous-time or discrete-time, is defined by its symmetry with its time-reversed version. Mathematically, this is represented as
Circuit Terminology01:14

Circuit Terminology

An electrical network is a system composed of interconnected elements, such as resistors, capacitors, inductors, and voltage or current sources. Unlike a circuit, an electrical network does not necessarily form a closed path. In other words, while all circuits can be considered networks due to their interconnected nature, not every network qualifies as a circuit.
A circuit, on the other hand, is also an interconnected system of electrical elements but must contain one or more closed paths.
Properties of Fourier series II01:21

Properties of Fourier series II

Time scaling of signals is a crucial concept in signal processing that affects the Fourier series representation without altering its coefficients. The process modifies the fundamental frequency, thereby changing how the series represents the signal over time. This principle is essential in various applications, including audio and image processing, where signal manipulation is frequent. Understanding function symmetries is fundamental to simplifying the Fourier series.
A function f(t) is...
Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
Network Function of a Circuit01:25

Network Function of a Circuit

Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.

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Related Experiment Video

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Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
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Detecting degree symmetries in networks.

Petter Holme1

  • 1Department of Computer Science, University of New Mexico, Albuquerque, New Mexico 87131, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 10, 2006
PubMed
Summary

We introduce degree symmetry, a network measure assessing path overlap around a vertex. Most networks exhibit weak positive degree symmetry, with notable exceptions in airport and social networks.

Area of Science:

  • Network Science
  • Graph Theory
  • Computational Biology

Background:

  • Network structures exhibit varying degrees of symmetry around vertices.
  • Understanding vertex neighborhood symmetry is crucial for network analysis.

Purpose of the Study:

  • To introduce and define a novel measure of vertex symmetry called degree symmetry.
  • To quantify degree symmetry in artificial and real-world networks, including the human metabolic network.
  • To analyze degree symmetry patterns across diverse network types.

Main Methods:

  • Derivation of mathematical measures for degree symmetry.
  • Evaluation of these measures on synthetic network models.
  • Application of measures to real-world networks, specifically the human metabolic network.

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  • Calculation of average degree-symmetry coefficients for various network classes.

    • Main Results:

    • Most analyzed real-world networks demonstrate weak positive degree symmetry.
    • Airport networks exhibit a negative degree-symmetry coefficient.
    • One-mode projections of social affiliation networks show strong positive degree symmetry.

    Conclusions:

    • Degree symmetry provides a quantifiable metric for vertex neighborhood structure.
    • Network types display distinct degree symmetry characteristics, offering insights into their organization.
    • Findings highlight the utility of degree symmetry in characterizing complex systems.