  A complete list of all connected arc-transitive asymmetric digraphs of
in-valence and out-valence 2 on up to 1000 vertices is presented. As a
byproduct, a complete list of all connected 4-valent graphs admitting a
half-arc-transitive group of automorphisms on up to 1000 vertices is obtained.
Several graph-theoretical properties of the elements of our census are
calculated and discussed.
