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

Abstract

Abstract Degree correlation plays a crucial role in studying network structures; however, its varied forms pose challenges to understanding its impact on network dynamics. In this study, a method is devised that uses eigenvalue decomposition to characterize degree correlations. Additionally, the applicability of this method is 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 social networks and their dynamics.