A simple Havel-Hakimi type algorithm to realize graphical degree sequences of directed graphs
One of the simplest ways to decide whether a given ﬁnite sequence of positive integers can arise as the degree sequence of a simple graph is the greedy algorithm of Havel and Hakimi. This note extends their approach to directed graphs. It also studies cases of some simple forbidden edge-sets. Finally, it proves a result which is useful to design an MCMC algorithm to ﬁnd random realizations of prescribed directed degree sequences.