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Layer degradation triggers an abrupt structural transition in multiplex networks.

Emanuele Cozzo1,2, Guilherme Ferraz de Arruda3, Francisco A Rodrigues4,5,6

  • 1Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Zaragoza 50009, Spain.

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|September 11, 2019
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Summary

Network robustness in multiplex networks shows a critical transition during layer degradation. This structural change reveals distinct phases of system resilience against link failures.

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Area of Science:

  • Network Science
  • Graph Theory
  • Complex Systems

Background:

  • Network robustness is crucial for understanding system resilience.
  • Multiplex networks, with multiple interacting layers, exhibit unique behaviors compared to single-layer networks.
  • Layer degradation, the loss of link weights, can significantly impact network structure and function.

Purpose of the Study:

  • To investigate the structural transitions in multiplex networks due to layer degradation.
  • To identify the critical conditions triggering abrupt changes in network algebraic connectivity.
  • To elucidate the relationship between layer degradation, intralayer link weights, and inter-layer coupling.

Main Methods:

  • Analysis of structural transitions in multiplex networks.
  • Mathematical determination of critical weight values for continuous layer degradation.
  • Investigation of the role of intralayer link weight and inter-layer coupling.

Main Results:

  • Layer degradation induces a structural transition marked by abrupt changes in algebraic connectivity.
  • Multiplex networks exhibit two distinct phases: one with layer-specific protection and another where failures propagate across all layers.
  • The critical intralayer link weight for transition is precisely determined and related to inter-layer coupling.

Conclusions:

  • Multiplex networks possess distinct resilience properties compared to single-layer systems.
  • Understanding critical transitions is key to designing robust multiplex networks.
  • The interplay between intralayer and interlayer properties governs network behavior under degradation.