Directed random graphs with given degree distributions

Given two distributions FF and GG on the nonnegative integers we propose an algorithm to construct in- and out-degree sequences from samples of i.i.d. observations from FF and GG, 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 FF and GG 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) FF and GG 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.