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Hurst analysis of dynamic networks.

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This study introduces multifractal analysis to explore network dynamics using Hurst integrals. Findings reveal complex fractal structures in real-world networks, particularly financial systems, offering new insights into system dynamics.

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Area of Science:

  • Complex systems analysis
  • Network science
  • Fractal geometry

Background:

  • Network snapshots over time effectively capture system dynamics.
  • Understanding fractal structures within dynamic networks is crucial for analyzing complex systems.

Purpose of the Study:

  • To develop and apply multifractal analysis to snapshot networks.
  • To investigate the presence and nature of fractal structures in dynamic network data.
  • To differentiate network dynamics using fractal characteristics.

Main Methods:

  • Construction of a multifractal analysis framework for snapshot networks.
  • Utilization of the Hurst integral to identify fractal patterns.
  • Comparative analysis with adjusted network models to interpret the Hurst exponent.
  • Examination of two real-world network datasets.

Main Results:

  • Snapshot networks exhibit multiple fractal structures, including local and global patterns.
  • The Hurst exponent effectively distinguishes rich dynamics within real snapshot networks.
  • Financial networks demonstrate significant multifractal dynamics.

Conclusions:

  • Multifractal analysis provides a novel perspective for studying dynamic networks.
  • The Hurst exponent is a valuable tool for characterizing complex system dynamics through fractal properties.
  • Real-world networks, especially financial ones, possess intricate multifractal dynamics.