  We classify isomorphism-invariant random digraphs according to where
randomness resides, namely, arcs, vertices, and vertices and arcs together
which in turn yield arc random digraphs (ARD), vertex random digraphs (VRD) and
vertex-arc random digraphs (VARD), respectively. This digraph classification
can be viewed as an extension of the classification of isomorphism-invariant
random graphs. We introduce randomness in the direction of the edges of a given
graph and obtain direction random digraphs (DRD) as well. We classify DRDs
according to which component is random in addition to the direction and study
the relations of DRDs with VARDs, VRDs and ARDs. We also consider random
nearest neighbor digraphs and determine their membership with respect to these
digraph families.
