  Positroids are matroids realizable by real matrices with all nonnegative
maximal minors. They partition the ordered matroids into equivalence classes,
called positroid envelope classes, by their Grassmann necklaces. We give an
explicit graph construction that shows that every positroid envelope class
contains a graphic matroid. We show that the following classes of positroids
are equivalent: graphic, binary, and regular, and that a graphic positroid is
the unique matroid in its positroid envelope class. Finally, we show that every
graphic positroid has an oriented graph representable by a signed incidence
matrix with all nonnegative minors.
