Assortative and disassortative mixing investigated using the spectra of graphs

TL;DR

This paper explores how degree correlations in networks influence their spectral properties, revealing universal patterns in short-range eigenvalue correlations and linking long-range correlations to network randomness, with implications for biological network degeneracies.

Contribution

It demonstrates the universal behavior of short-range eigenvalue correlations across different network types and connects long-range correlations to the degree of randomness in assortative and disassortative networks.

Findings

Short-range eigenvalue correlations follow universal RMT predictions.

Long-range correlations indicate the level of randomness in the network.

Biological networks show high degeneracy at zero eigenvalues.

Abstract

We investigate the impact of degree-degree correlations on the spectra of networks. Even though density distributions exhibit drastic changes depending on the (dis)assortative mixing and the network architecture, the short range correlations in eigenvalues exhibit universal RMT predictions. The long range correlations turn out to be a measure of randomness in (dis)assortative networks. The analysis further provides insight in to the origin of high degeneracy at the zero eigenvalue displayed by majority of the biological networks.