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Area of Science:

  • Network Science
  • Random Matrix Theory
  • Statistical Physics

Background:

  • Eigenvalue spacing distributions are crucial for understanding spectral properties in many-body systems.
  • Random matrix theory provides tools to analyze complex system spectra.
  • Network architecture influences spectral properties.

Purpose of the Study:

  • To numerically investigate the eigenvalue ratios distribution in various network models.
  • To analyze the effect of diagonal disorder on these distributions.
  • To relate the critical disorder strength to network properties and dynamics.

Main Methods:

  • Numerical investigation of eigenvalue ratios distribution.
  • Analysis of small-world, Erdős-Rényi, and (dis)assortative random networks.
  • Introduction of diagonal disorder in adjacency matrices.
  • Relating critical disorder to maximum entropy random walker steady-state time.

Main Results:

  • Without disorder, networks exhibit Gaussian orthogonal ensemble (GOE) statistics.
  • Diagonal disorder induces a transition from GOE to Poisson statistics.
  • Critical disorder strength increases with network randomness.
  • Critical disorder is linked to random walker relaxation time.

Conclusions:

  • Diagonal disorder significantly alters spectral properties of network models.
  • The transition to Poisson statistics is a key indicator of disorder effects.
  • Understanding these transitions is vital for analyzing network dynamics and transient behaviors.