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

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.