  The minimum rank of a simple graph $G$ is the smallest possible rank over all
symmetric real matrices $A$ whose nonzero off-diagonal entries correspond to
the edges of $G$. Using the zero forcing number, we prove that the minimum rank
of the butterfly network is $\frac19\left[(3r+1)2^{r+1}-2(-1)^r\right]$ and
that this is equal to the rank of its adjacency matrix.
