  For a planar directed graph G, Postnikov's boundary measurement map sends
positive weight functions on the edges of G onto the appropriate totally
nonnegative Grassmann cell. We establish an explicit formula for Postnikov's
map by expressing each Pluecker coordinate as a ratio of two combinatorially
defined polynomials in the edge weights, with positive integer coefficients. In
the non-planar setting, we show that a similar formula holds for special
choices of Pluecker coordinates.
