Spectral similarity for Barab\'asi-Albert and Chung-Lu models

TL;DR

This paper investigates the spectral similarities and differences between Barabási-Albert and Chung-Lu network models, revealing conditions for spectral distribution similarity and highlighting differences in extreme eigenvalues and eigenvectors, with applications in spectral graph theory and quantum search.

Contribution

The study provides a detailed spectral comparison of the two models, identifying when their spectral distributions align and when they diverge, which was not previously characterized.

Findings

Spectral distributions are similar for large Barabási-Albert parameters.

Extreme eigenvalues and principal eigenvectors differ between models.

Results have implications for spectral graph theory and quantum spatial search efficiency.

Abstract

In the paper we have analyzed spectral similarity between Barab\'asi-Albert and Chung-lu models. We have shown the similarity of spectral distribution for sufficiently large Barab\'asi-Albert parameter value. Contrary, extreme eigenvalues and principal eigenvector are not similar for those model. We provide applications of obtained results related to the spectral graph theory and efficiency of quantum spatial search