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Limited path percolation in complex networks.

Eduardo López1, Roni Parshani, Reuven Cohen

  • 1CNLS & T-7, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. edlopez@lanl.gov

Physical Review Letters
|November 13, 2007
PubMed
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Network communication stability is assessed by link removal, revealing a new percolation transition. Above this critical point, networks maintain communication; below it, communication significantly degrades.

Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Network communication relies on connectivity and shortest paths.
  • Link removal can disrupt network functionality and information flow.
  • Maintaining communication efficiency under network degradation is crucial for many applications.

Purpose of the Study:

  • To investigate the impact of link removal on network communication stability.
  • To identify and characterize a new percolation transition related to path length constraints.
  • To determine the critical fraction of remaining links for effective network communication.

Main Methods:

  • Analytical calculations of network properties.
  • Numerical simulations to validate theoretical findings.

Related Experiment Videos

  • Analysis of shortest path lengths before and after link removal.

    • Main Results:

    • A novel percolation transition was identified at p(c)=(kappa(0)-1)((1-a)/a).
    • Above the critical point p(c), a significant portion of nodes maintain communication within scaled shortest path limits.
    • Below p(c), network communication effectiveness drastically decreases.

    Conclusions:

    • The study reveals a new threshold for network communication resilience.
    • Findings have implications for designing robust networks and efficient routing algorithms.
    • The results are relevant for strategies in network design and immunization.