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Hidden transition in multiplex networks.

R A da Costa1, G J Baxter2, S N Dorogovtsev2

  • 1Department of Physics & I3N, University of Aveiro, Aveiro, Portugal. americo.costa@ua.pt.

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Summary
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Weak multiplex percolation in multi-layer networks exhibits a novel, abrupt phase transition. Removing a small fraction of nodes or edges can cause catastrophic network collapse or stability, independent of the giant component size.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Percolation theory studies the connectivity of random networks.
  • Multiplex networks consist of multiple layers of connections.
  • Weak multiplex percolation extends percolation to these multi-layer systems.

Purpose of the Study:

  • To investigate phase transitions in weak multiplex percolation.
  • To characterize a novel discontinuous phase transition.
  • To analyze the dynamics of network collapse and stability.

Main Methods:

  • Theoretical analysis of multi-layer networks with three or more layers.
  • Identification of a control parameter: fraction of single-connected nodes per layer.
  • Derivation of asymptotic expressions for collapse and relaxation times.

Main Results:

  • A novel discontinuous phase transition was identified in weak multiplex percolation.
  • This transition occurs above a critical control parameter value.
  • Failure cascades can lead to total network collapse or return to stability, without affecting the giant component singularity.

Conclusions:

  • The study reveals an anomalous discontinuous transition in multi-layer networks.
  • Network resilience is highly sensitive to small perturbations near the critical point.
  • Asymptotic formulas describe the time dynamics of collapse and relaxation.