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This study introduces a new analytic theory for percolation in complex networks, explaining how network structure and component sizes change during degradation. The theory predicts phase transitions and critical behaviors, aiding in network design and collapse detection.

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Area of Science:

  • Complex networks
  • Network science
  • Statistical physics

Background:

  • Percolation models network degradation and reveals network structure peculiarities.
  • Network properties undergo transformations, including phase transitions, during percolation.
  • Subtle local changes in degree distribution cause global network transformations.

Purpose of the Study:

  • To establish a generic analytic theory for simple and color-dependent bond percolation.
  • To describe how network structure and connected component sizes are affected by percolation.
  • To predict phase transition locations and critical regimes.

Main Methods:

  • Development of a generic analytic theory.
  • Analysis of simple and color-dependent bond percolation processes.
  • Investigation of connected component structures and sizes.

Main Results:

  • The theory predicts phase transition locations and the existence of wide critical regimes.
  • It describes how network structure and component sizes are affected by percolation.
  • A phenomenon of color switching in small components is identified.

Conclusions:

  • The developed theory provides a comprehensive understanding of percolation effects on complex networks.
  • Results can inform the design of percolation-like processes and network optimization.
  • The findings aid in detecting early signals of network collapse.