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Localization of multilayer networks by optimized single-layer rewiring.

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We investigated how to localize principal eigenvectors (PEVs) in multilayer networks (MNs) by rewiring edges. A single rewiring can drastically alter PEV localization, offering insights into network dynamics and perturbation propagation.

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Area of Science:

  • Network Science
  • Graph Theory
  • Spectral Analysis

Background:

  • Multilayer networks (MNs) exhibit complex behaviors influenced by their structure.
  • Principal eigenvectors (PEVs) play a crucial role in understanding network properties, including information flow and stability.
  • Localization of PEVs can indicate concentrated influence or activity within specific network components.

Purpose of the Study:

  • To investigate the localization properties of principal eigenvectors (PEVs) in multilayer networks (MNs).
  • To develop and apply an optimization technique for rewiring network edges to achieve PEV localization.
  • To understand the relationship between network structure, spectral properties, and PEV localization.

Main Methods:

  • Employing an optimization technique to rewire edges of a multilayer network.
  • Analyzing structural and spectral properties during the edge rewiring process.
  • Comparing simulation results with real-world social and biological network data.

Main Results:

  • Achieving a highly localized PEV in a multilayer network by rewiring only a single layer.
  • Demonstrating that a single edge rewiring can cause complete delocalization of a previously localized PEV.
  • Observing that high sensitivity in PEV localization correlates with the second largest eigenvalue being close to the largest one.
  • Validating simulation findings with real-world multilayer network data.

Conclusions:

  • PEV localization in multilayer networks is highly sensitive to structural modifications.
  • The spectral proximity of eigenvalues offers insights into the origins of PEV localization.
  • The findings are relevant for applications involving perturbation propagation in complex networks.