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General theory for extended-range percolation on simple and multiplex networks.

Lorenzo Cirigliano1,2, Claudio Castellano2,3, Ginestra Bianconi4,5

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Extended-range percolation, crucial for quantum communication, enhances network robustness. A new theory explains how trusted and untrusted nodes form resilient communication pathways, even in complex interdependent networks.

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Area of Science:

  • Statistical physics
  • Network science
  • Quantum information theory

Background:

  • Percolation theory describes connectivity in random networks.
  • Extended-range percolation allows untrusted nodes to facilitate communication.
  • Understanding network robustness is vital for secure communication systems.

Purpose of the Study:

  • To develop a general theory for extended-range percolation.
  • To analyze extended-range percolation on interdependent multiplex networks.
  • To investigate the interplay between robustness and fragility in complex networks.

Main Methods:

  • Developed a general theory based on a message-passing algorithm.
  • Valid for arbitrary range R in locally treelike networks.
  • Investigated interdependent multiplex networks.

Main Results:

  • The theory accurately describes extended-range percolation properties.
  • Interplay of extended-range effects and interdependencies yields a rich phase diagram.
  • Discontinuous phase transitions and reentrant phases were observed.

Conclusions:

  • The developed theory provides a fundamental reference for extended-range path models.
  • Extended-range percolation enhances multiplex network robustness against failures.
  • Interdependencies introduce fragility, leading to complex phase behaviors.