Generation of arbitrarily two-point correlated random networks

Random networks are intensively used as null models to investigate properties of complex networks. We describe an efficient and accurate algorithm to generate arbitrarily two-point correlated undirected random networks without self- or multiple-edges among vertices. With the goal to systematically investigate the influence of two-point correlations, we furthermore develop a formalism to construct a joint degree distribution $P(j,k)$ which allows to fix an arbitrary degree distribution $P(k)$ and an arbitrary average nearest neighbor function $\text{knn}(k)$ simultaneously. Using the presented algorithm, this formalism is demonstrated with scale-free networks ($P(k)\propto k^{-\gamma }$) and empirical complex networks ($P(k)$ taken from network) as examples. Finally, we generalize our algorithm to annealed networks which allows networks to be represented in a mean-field like manner.