  Wilson loop diagrams are an important tool in studying scattering amplitudes
of SYM $N=4$ theory and are known by previous work to be associated to
positroids. In this paper we study the structure of the associated positroids,
as well as the structure of the denominator of the integrand defined by each
diagram. We give an algorithm to derive the Grassmann necklace of the
associated positroid directly from the Wilson loop diagram, and a recursive
proof that the dimension of these cells is thrice the number of propagators in
the diagram. We also show that the ideal generated by the denominator in the
integrand is the radical of the ideal generated by the product of Grassmann
necklace minors.
