Modeling the Evolution of Degree Correlation in Scale-Free Topology Generators

In this paper, the authors examine the asymptotic behavior of degree correlation (i.e., the joint degree distribution of adjacent nodes) in several scale-free topology generators GED, PLRG, GLP, BA, AB. They present a unifying analytical framework that allows tractable analysis of degree correlation in all studied models and derive asymptotic formulas of two degree correlation metrics - assortativity and clustering. The authors' results indicate that all studied generators become uncorrelated as graph size increases, which is inconsistent with time-invariance of these metrics in real networks such as the Internet.