Here's two random $(0,1)$-matrices: $$ A= \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 1 \\ \end{bmatrix} \qquad B= \begin{bmatrix} 1 & 1 \\ 0 & 1 \\ \end{bmatrix}. $$ They can be interpreted as biadjacency matrices: the graph $G[A]$ has vertices $\{r_1,r_2\} \cup \{c_1,c_2,c_3\}$ and undirected edges $r_i c_j$ if and only if $A[i,j]=1$, and likewise for $B$.

If we take a Kronecker product of $A$ and $B$, we obtain: $$ A \otimes B=\begin{bmatrix} \color{red} 1 & \color{red} 1 & 0 & 0 & 0 & 0\\ \color{red} 0 & \color{red} 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & \color{blue} 1 & \color{blue} 1 & \color{green} 1 & \color{green} 1 \\ 0 & 0 & \color{blue} 0 & \color{blue} 1 & \color{green} 0 & \color{green} 1 \\ \end{bmatrix} $$ And thus we have a bipartite graph $G[A \otimes B]$ with biadjacency matrix $A \otimes B$.

While I feel like this would have been studied, I don't know what this graph is called. I didn't find it on Wikipedia's list: the vertex set is *not* $V(G[A]) \times V(G[B])$.

**Question**: The Kronecker product of two bipartite graphs' biadjacency matrices: what's it called?