Construction of Directed 2K Graphs

We study the problem of generating synthetic graphs that resemble real-world directed graphs in terms of their degree correlations. In order to capture degree correlation specifically for directed graphs, we define directed 2K (D2K) as those graphs with a given directed degree sequence (DDS) and a given target joint degree and attribute matrix (JDAM). We provide necessary and sufficient conditions for a target D2K to be realizable and we design an efficient algorithm that generates graph realizations with exactly the target D2K. We apply our algorithm to generate synthetic graphs that target real-world directed graphs (such as Twitter), and we demonstrate its benefits compared to state-of-the-art construction algorithms.