  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.
