  Degree correlation is an important topological property common to many
real-world networks. In this paper, the statistical measures for characterizing
the degree correlation in networks are investigated analytically. We give an
exact proof of the consistency for the statistical measures, reveal the general
linear relation in the degree correlation, which provide a simple and
interesting perspective on the analysis of the degree correlation in complex
networks. By using the general linear analysis, we investigate the perturbation
of the degree correlation in complex networks caused by the addition of few
nodes and the rich club. The results show that the assortativity of homogeneous
networks such as the ER graphs is easily to be affected strongly by the simple
structural changes, while it has only slight variation for heterogeneous
networks with broad degree distribution such as the scale-free networks.
Clearly, the homogeneous networks are more sensitive for the perturbation than
the heterogeneous networks.
