  In this paper, we study a new application of the positive Grassmanian to
Wilson loop diagrams (or MHV diagrams) for scattering amplitudes in N=4 Super
Yang-Mill theory ($N=4$ SYM). There has been much interest in studying this
theory via the positive Grassmanians using BCFW recursion. This is the first
attempt to study MHV diagrams for planar Wilson loop calculations (or planar
amplitudes) in terms of positive Grassmannians. We codify Wilson loop diagrams
completely in terms of matroids. This allows us to apply the combinatorial
tools in matroid theory used to identify positroids, (non-negative
Grassmannians), to Wilson loop diagrams. In doing so, we find that certain
non-planar Wilson loop diagrams define positive Grassmannians. While non-planar
diagrams do not have physical meaning, this finding suggests that they may have
value as an algebraic tool, and deserve further investigation.
