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We introduce the link-space formalism for analyzing network models withdegree-degree correlations. The formalism is based on a statistical descriptionof the fraction of links l_{i,j} connecting nodes of degrees i and j. Todemonstrate its use, we apply the framework to some pedagogical network models,namely, random-attachment, Barabasi-Albert preferential attachment and theclassical Erdos and Renyi random graph. For these three models the link-spacematrix can be solved analytically. We apply the formalism to a simpleone-parameter growing network model whose numerical solution exemplifies theeffect of degree-degree correlations for the resulting degree distribution. Wealso employ the formalism to derive the degree distributions of two very simplenetwork decay models, more specifically, that of random link deletion andrandom node deletion. The formalism allows detailed analysis of thecorrelations within networks and we also employ it to derive the form of aperfectly non-assortative network for arbitrary degree distribution.

Link-space formalism for network analysis