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Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
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Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms
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An Extended Correlation Dimension of Complex Networks.

Sheng Zhang1, Wenxiang Lan1, Weikai Dai1

  • 1School of Information Engineering, Nanchang Hangkong University, 696 Fenghe South Avenue, Nanchang 330063, China.

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Summary

This study extends the correlation dimension to analyze fractal properties in weighted complex networks. The new method effectively quantifies fractal scaling and small-world effects in both weighted and unweighted networks.

Keywords:
correlation dimensionfractal propertysmall-world networkweighted networks

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Area of Science:

  • Complex networks analysis
  • Network science
  • Fractal geometry

Background:

  • Fractal and self-similarity are key features of complex networks.
  • The correlation dimension measures fractal nature in unweighted networks but lacks extension to weighted networks.

Purpose of the Study:

  • To extend the correlation dimension method for analyzing fractal properties in weighted complex networks.
  • To validate the proposed method on synthetic and real-world weighted networks.
  • To compare the correlation dimension's suitability for analyzing small-world effects against other fractal dimensions.

Main Methods:

  • Developed a novel method to extend the correlation dimension to weighted networks.
  • Utilized edge-weight accumulation to determine scale distances.
  • Applied the method to six diverse networks, including synthetic fractal and real-world weighted networks.

Main Results:

  • The extended correlation dimension method proved effective for fractal scaling analysis in weighted complex networks.
  • The method successfully analyzed the fractal properties of Newman-Watts (NW) unweighted small-world networks.
  • Correlation dimension showed greater suitability for quantitative analysis of small-world effects compared to other fractal dimensions.

Conclusions:

  • The proposed correlation dimension method is a robust tool for analyzing fractal scaling in weighted complex networks.
  • This approach enhances the understanding of fractal characteristics in network science.
  • The correlation dimension offers a more precise measure for quantifying small-world network properties.