  This paper solves a problem that was stated by M. A. Harrison in
1973~\cite{harrison1973number}. This problem, that has remained open since then
is concerned with counting equivalence classes of $n\times r$ binary matrices
under row and column permutations. Let $I$ and $O$ denote two sets of vertices,
where $I\cap O =\Phi$, $|I| = n$, $|O| = r$, and $B_u(n,r)$ denote the set of
unlabeled graphs whose edges connect vertices in $I$ and $O$. Harrison
established that the number of equivalence classes of $n\times r$ binary
matrices is equal to the number of unlabeled graphs in $B_u(n,r).$ He also
computed the number of such matrices (hence such graphs) for small values of
$n$ and $r$ without providing an asymptotic formula $|B_u(n,r)|.$ Here, such an
asymptotic formula is provided by proving the following two-sided equality
using Polya's Counting Theorem.
