Let the adjacency matrix of an *undirected bipartite* graph be $A = \begin{pmatrix} 0 & B \\ B^T & 0 \end{pmatrix}$ where B is called the *biadjacency matrix*.

Now, by instead interpreting B as an *adjacency matrix* of an *non-bipartite (arbitrary) directed* graph, we get an equivalence relation between the bipartite undirected graph (with *bi*adjacency matrix B) and the arbitrary directed graph (with adjacency matrix B).

Does this equivalence have a name? Is it discussed somewhere in literature? Thank you!