  Many networks contain correlations and often conventional analysis is
incapable of incorporating this often essential feature. In arXiv:0708.2176, we
introduced the link-space formalism for analysing degree-degree correlations in
evolving networks. In this extended version, we provide additional mathematical
details and supplementary material.
  We explore some of the common oversights when these correlations are not
taken into account, highlighting the importance of the formalism. 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.
