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Epidemic spreading on complex networks with community structures.

Clara Stegehuis1, Remco van der Hofstad1, Johan S H van Leeuwaarden1

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Community structure in networks significantly impacts diffusion processes like information or virus spreading. The mesoscopic organization of communities, not their internal details, is key to understanding these network behaviors.

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Area of Science:

  • Network Science
  • Complex Systems
  • Statistical Physics

Background:

  • Real-world networks often exhibit community structures.
  • Understanding these structures is crucial for modeling network dynamics.

Purpose of the Study:

  • To investigate the role of community structure in network percolation processes.
  • To develop random graph models that preserve community properties.

Main Methods:

  • Studied two random graph models for network generation.
  • One model preserves exact community structure; the other preserves community sets and vertex degrees.
  • Analyzed the impact on percolation processes (e.g., diffusion, spreading).

Main Results:

  • Community structure significantly influences diffusion and spreading dynamics.
  • It can either facilitate or hinder these processes.
  • The mesoscopic organization of communities is more critical than their internal details.

Conclusions:

  • Network community structure is a key determinant of percolation behavior.
  • The overall community organization, rather than fine-grained internal structure, dictates diffusion patterns.
  • Relative community denseness may explain insensitivity to internal structure.