Representation of degree correlation using eigenvalue decomposition and its application to epidemic models

TL;DR

This paper introduces an eigenvalue decomposition method to characterize degree correlations in networks and demonstrates its application in approximating epidemic model parameters, enhancing understanding of network dynamics.

Contribution

It presents a novel eigenvalue-based approach to quantify degree correlations and applies it to epidemic models, linking network structure to epidemic behavior.

Findings

Eigenvalue decomposition effectively characterizes degree correlations.

The method approximates basic and reproduction numbers in epidemic networks.

Degree correlations significantly influence epidemic dynamics.

Abstract

Degree correlation plays a crucial role in studying network structures; however, its varied forms pose challenges to understanding its impact on network dynamics. This study devised a method that uses eigenvalue decomposition to characterize degree correlations. Additionally, the applicability of this method was demonstrated by approximating the basic and type reproduction numbers in an epidemic network model. The findings elucidate the interplay between degree correlations and epidemic behavior, thus contributing to a deeper understanding of complex networks and their dynamics.