The digraph intersection of two digraphs is the digraph whose vertex set (respectively, edge set) is the intersection of their vertex sets (respectively, edge sets).
If 
is a positive integer, then the adjacency
matrix of the digraph intersection of two labeled 
-digraphs is the Hadamard product (a.k.a. entrywise product)
of their adjacency matrices.
If 
is a positive integer, then the labeled 
-digraphs form a semilattice with respect
to the digraph intersection.
