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One of the simplest ways to decide whether a given finite sequence ofpositive integers can arise as the degree sequence of a simple graph is thegreedy algorithm of Havel and Hakimi. This note extends their approach todirected 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 findrandom realizations of prescribed directed degree sequences.

A simple Havel-Hakimi type algorithm to realize graphical degree sequences of directed graphs