Effect of Unfolding on the Spectral Statistics of Adjacency Matrices of Complex Networks

TL;DR

This paper investigates how the process of spectral unfolding affects the analysis of spectral statistics in complex network adjacency matrices, revealing that spectral rigidity is more sensitive to unfolding than eigenvalue spacing distribution.

Contribution

It provides a detailed analysis of the impact of spectral unfolding on spectral statistics, highlighting the differential sensitivity of spectral measures in complex networks.

Findings

Spacing distribution is largely unaffected by unfolding methods.

Spectral rigidity shows significant sensitivity to the unfolding process.

Unfolding choice can influence spectral analysis outcomes in network studies.

Abstract

Random matrix theory is finding an increasing number of applications in the context of information theory and communication systems, especially in studying the properties of complex networks. Such properties include short-term and long-term correlation. We study the spectral fluctuations of the adjacency of networks using random-matrix theory. We consider the influence of the spectral unfolding, which is a necessary procedure to remove the secular properties of the spectrum, on different spectral statistics. We find that, while the spacing distribution of the eigenvalues shows little sensitivity to the unfolding method used, the spectral rigidity has greater sensitivity to unfolding.