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Decomposing the Variance in Reading Comprehension to Reveal the Unique and Common Effects of Language and Decoding
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Normalised degree variance.

Keith M Smith1,2, Javier Escudero3

  • 1Centre for Medical Informatics, Usher Institute, University of Edinburgh, 9 Edinburgh Bioquarter, Edinburgh, EH16 4UX UK.

Applied Network Science
|July 7, 2020
PubMed
Summary
This summary is machine-generated.

A new, analytically valid normalization for degree variance in network science is introduced. This method is unbiased by network size and density, improving cross-disciplinary comparisons of network structures.

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Area of Science:

  • Network Science
  • Graph Theory
  • Data Analysis

Background:

  • Network science studies require unbiased graph indices for comparability across disciplines.
  • Degree variance is a key metric for network degree heterogeneity, but existing normalizations have limitations.

Purpose of the Study:

  • To introduce an analytically valid normalization for degree variance.
  • To provide a metric unbiased by network size and density for enhanced comparability.
  • To offer a computationally efficient and mathematically straightforward analysis tool.

Main Methods:

  • Developed a closed-form expression for normalizing degree variance.
  • Validated the normalization across various network models: Erdös-Rényi (ER) random graphs, random geometric graphs, scale-free networks, random hierarchy networks, and resting-state brain networks.
  • Analyzed 184 real-world binary networks from diverse scientific domains.

Main Results:

  • The proposed normalization yields equal values for graphs and their complements.
  • The normalization is maximal in star graphs and their complements.
  • Its expected value is constant with respect to density in ER random graphs.
  • Demonstrated reduced sensitivity to network size and density compared to previous methods.
  • Found normalized degree variance is uncorrelated with average degree and robust to subsampling.
  • Identified greater degree heterogeneity in brain connectomes and food webs than protein interaction networks.

Conclusions:

  • The new degree variance normalization offers a robust, efficient, and widely applicable tool for network science.
  • It enhances the comparability of network structures across different fields and network types.
  • The findings reveal distinct patterns of degree heterogeneity in biological networks.