OK. It's possible to adapt that final example, with a bit of messing around.
The product
∣E∣=i=j∏∣Eij∣ would enumerate all possible digraphs, but include ones where you had directed edges
ei,j as well as
ej,i, i.e. 2-loops, which are not allowed.
So how to remove these - perhaps this what you were aiming at originally.
One way is to rearrange our original product and pair up the sets. Since
i=j∣E∣=i=j∏∣Eij∣=i<j∏∣EijEji∣And restrict the number of combinations in our product
∣Ei,jEj,i∣ to just valid combinations for a digraph, i.e. just 3.