Let $M$ be an $n \times n$-matrix with entries only 0 or 1. Let $R$ be the same matrix as $M$ but with all diagonal entries set to zero. Let $U=(u_{i,j})$ be the matrix with 1 as an entry if $R^2=R *R$ (the matrix product of $R$ with itself) has a non-zero entry in the same position and let $U$ have 0 in this entry if $R^2$ has 0 as an entry in this position.
Let $G_M$ be the directed graph with $n$ vertices and there is an arrow from $i$ to $j$ if and only if $u_{i,j}$ is 1.
My question is whether there is a quick method to obtain all 0-1 matrices with Sage for a given $n$ and the associated graph $G_M$.