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Related Concept Videos

Law of Independent Assortment02:03

Law of Independent Assortment

While Mendel’s Law of Segregation states that the two alleles for one gene are separated into different gametes, a different question of how different genes are inherited remains. For example, is the gene for tall plants inherited with the gene for green peas? Mendel asked this question by experimenting with a dihybrid cross; a cross in which both parents are homozygous for two distinct traits resulting in an F1 generation that are heterozygous for both traits.
Law of Independent Assortment02:03

Law of Independent Assortment

While Mendel’s Law of Segregation states that the two alleles for one gene are separated into different gametes, a different question of how different genes are inherited remains. For example, is the gene for tall plants inherited with the gene for green peas? Mendel asked this question by experimenting with a dihybrid cross; a cross in which both parents are homozygous for two distinct traits resulting in an F1 generation that are heterozygous for both traits.
Skewness01:06

Skewness

The measures of central tendency calculated from a data set may not reveal much about its intrinsic distribution. If a plot is made of the data set’s values, the mean and the median may not only differ, but also the plot may have more values on one side of the central tendencies. Such a data set is said to be skewed towards that side.
The longer the tail of the plot on one side, the more skewed it is. The skewness of a data set’s values suggests that the measures of central tendency are...
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...
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...
Graphical and Analytic Representation of Sinusoids01:20

Graphical and Analytic Representation of Sinusoids

Analyzing two sinusoidal voltages with equal amplitude and period but different phases on an oscilloscope, an instrument used to display and analyze waveforms, involves a three-step process.
The first step is measuring the peak-to-peak value, which is twice the amplitude of the sinusoid. This provides information about the maximum voltage swing of the waveform.
Secondly, the period and angular frequency are determined. The period is the time taken for one complete cycle of the waveform, while...

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Updated: Jun 5, 2026

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients
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Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients

Published on: December 18, 2016

Spectral graph analysis of modularity and assortativity.

P Van Mieghem1, X Ge, P Schumm

  • 1Faculty of Electrical Engineering, Mathematics, and Computer Science, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands. p.f.a.vanmieghem@tudelft.nl

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
PubMed
Summary
This summary is machine-generated.

This study presents Newman

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Area of Science:

  • Network science
  • Graph theory
  • Data analysis

Background:

  • Understanding network structure is crucial in various scientific fields.
  • Modularity is a key metric for assessing community structure in networks.
  • Assortativity influences network topology and function.

Purpose of the Study:

  • To derive expressions and bounds for Newman's modularity.
  • To investigate the relationship between spectral properties of the modularity matrix and maximum modularity.
  • To analyze the impact of varying graph assortativity on network properties.

Main Methods:

  • Derivation of theoretical expressions for Newman's modularity.
  • Analysis of the modularity matrix spectrum.
  • Degree-preserving rewiring to alter graph assortativity.
  • Computational simulations to observe network property changes.

Main Results:

  • Established conditions and properties for maximum network modularity.
  • Demonstrated that increasing assortativity enhances maximum modularity.
  • Observed a decrease in the number of clusters with rising assortativity.
  • Found that average hop count and effective graph resistance increase with assortativity.

Conclusions:

  • Assortativity is a significant factor influencing network modularity and community structure.
  • Network assortativity impacts global network properties like path lengths and resistance.
  • The findings provide insights into optimizing network design and analysis based on assortativity.