  Uniform sampling of simple graphs having a given degree sequence is a known
problem with exponential complexity in the square of the mean degree. For
undirected graphs, randomised approximation algorithms have nonetheless been
shown to achieve almost linear expected complexity for this problem. Here we
discuss the sequential stub matching for directed graphs and show that this
process can be mould to sample simple digraphs with asymptotically equal
probability. The process starts with an empty edge set and repeatedly adds
edges to it with a certain state-dependent bias until the desired degree
sequence is fulfilled, while avoiding placement of a double edge or self loop.
We show that uniform sampling is achieved in the sparse regime, when the
maximum degree $d_\text{max}$ is asymptotically dominated by $m^{1/4}$, where
$m$ is the number of edges. The proof is based on deriving various
combinatorial estimates related to the number of digraphs with a given directed
degree sequence and controlling concentration of these estimates in large
digraphs. This suggests that the sequential stub matching can be viewed as a
practical algorithm for almost uniform sampling of digraphs, and we show that
this algorithm can be implemented to feature linear expected runtime $O(m)$.
