Recently I have been trying to find a succinct algorithm for generation of disassortative networks. The best I have found is the algorithm by Newman described in his paper "Mixing patterns in networks" 2003.
The algorithm is based on the matrix $E = \{ e_{jk} \}$ where $e_{jk}$ is the fraction of edges that connect vertices of excess (remaining) degrees $j$ and $k$.
The algorithm is not in my favor because it has several significant pitfalls. My goal is to find the algorithm that given the order of the graph $n$ and the assortativity correlation coefficient $\rho(G)$ simulates a random graph with this value of $\rho$.