  Degree distributions are arguably the most important property of real world
networks. The classic edge configuration model or Chung-Lu model can generate
an undirected graph with any desired degree distribution. This serves as a good
null model to compare algorithms or perform experimental studies. Furthermore,
there are scalable algorithms that implement these models and they are
invaluable in the study of graphs. However, networks in the real-world are
often directed, and have a significant proportion of reciprocal edges. A
stronger relation exists between two nodes when they each point to one another
(reciprocal edge) as compared to when only one points to the other (one-way
edge). Despite their importance, reciprocal edges have been disregarded by most
directed graph models.
  We propose a null model for directed graphs inspired by the Chung-Lu model
that matches the in-, out-, and reciprocal-degree distributions of the real
graphs. Our algorithm is scalable and requires $O(m)$ random numbers to
generate a graph with $m$ edges. We perform a series of experiments on real
datasets and compare with existing graph models.
