  Given two distributions F and G on the nonnegative integers we propose an
algorithm to construct in- and out-degree sequences from samples of i.i.d.
observations from F and G, respectively, that with high probability will be
graphical, that is, from which a simple directed graph can be drawn. We then
analyze a directed version of the configuration model and show that, provided
that F and G have finite variance, the probability of obtaining a simple graph
is bounded away from zero as the number of nodes grows. We show that
conditional on the resulting graph being simple, the in- and out-degree
distributions are (approximately) F and G for large size graphs. Moreover, when
the degree distributions have only finite mean we show that the elimination of
self-loops and multiple edges does not significantly change the degree
distributions in the resulting simple graph.
