Abstract
Phys. Rev. E 77, 036112 (2008) We introduce the link-space formalism for analyzing network models with
degree-degree correlations. The formalism is based on a statistical description
of the fraction of links l_{i,j} connecting nodes of degrees i and j. To
demonstrate its use, we apply the framework to some pedagogical network models,
namely, random-attachment, Barabasi-Albert preferential attachment and the
classical Erdos and Renyi random graph. For these three models the link-space
matrix can be solved analytically. We apply the formalism to a simple
one-parameter growing network model whose numerical solution exemplifies the
effect of degree-degree correlations for the resulting degree distribution. We
also employ the formalism to derive the degree distributions of two very simple
network decay models, more specifically, that of random link deletion and
random node deletion. The formalism allows detailed analysis of the
correlations within networks and we also employ it to derive the form of a
perfectly non-assortative network for arbitrary degree distribution.
