Exploring universality of the β-Gaussian ensemble in complex networks via intermediate eigenvalue statistics

Area of Science:

• Statistical Physics
• Network Science
• Complex Systems

Background:

• Eigenvalue statistics are crucial for understanding transitions in physical systems, like localization-delocalization.
• The β-Gaussian ensemble is a recent, single-parameter model for intermediate eigenvalue statistics.

Purpose of the Study:

• To investigate the universality of the β-Gaussian ensemble in complex networks.
• To compare eigenvalue statistics of various network models with the β-Gaussian ensemble.

Main Methods:

• Studied eigenvalue statistics of small-world, Erdős-Rényi random, and scale-free networks.
• Compared nearest-neighbor and higher-order intermediate eigenvalue statistics with the β-Gaussian ensemble.

Main Results:

• Nearest-neighbor eigenvalue statistics of all studied networks agreed well with the β-Gaussian ensemble.
• The β-Gaussian ensemble showed limitations in describing higher-order intermediate eigenvalue statistics (n≥4).
• Nearest-neighbor statistics of the β-Gaussian ensemble matched higher-order intermediate statistics of the networks.

Conclusions:

• The β-Gaussian ensemble shows promise for nearest-neighbor eigenvalue statistics in complex networks.
• Further development is needed for the β-Gaussian ensemble to capture higher-order eigenvalue statistics accurately.
• The study highlights the potential and limitations of the β-Gaussian ensemble in network analysis.