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Controlling the Multifractal Generating Measures of Complex Networks.

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This study introduces a weighted multifractal graph model to analyze complex networks, revealing self-similar structures in biological and brain networks. The model aids in understanding network complexity and developing control strategies.

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Area of Science:

  • Complex systems science
  • Network science
  • Mathematical modeling

Background:

  • Real-world complex networks exhibit self-repeating patterns and multifractality.
  • Understanding multifractal behavior is crucial for characterizing network architecture and principles.

Purpose of the Study:

  • To propose and validate a weighted multifractal graph model for characterizing spatiotemporal complexity and heterogeneity in real networks.
  • To analyze the multifractal properties of biological and brain networks using the proposed model.

Main Methods:

  • Development of a weighted multifractal graph model.
  • Analytical verification of multifractal properties.
  • Application and analysis of the model to yeast cell chromosome interactions and human brain networks.

Main Results:

  • The model can reproduce diverse multifractal spectrums by adjusting parameters.
  • The model successfully characterizes chromosome and brain networks.
  • The model distinguishes between different network structures and states (e.g., healthy vs. mild cognitive impairment).

Conclusions:

  • The weighted multifractal graph model offers a novel approach to understanding self-similar structures in complex networks.
  • The model provides tools for network discrimination and the development of new network design and control strategies.