  Gaussian graphical models are parametric statistical models for jointly
normal random variables whose dependence structure is determined by a graph. In
previous work, we introduced trek separation, which gives a necessary and
sufficient condition in terms of the graph for when a subdeterminant is zero
for all covariance matrices that belong to the Gaussian graphical model. Here
we extend this result to give explicit cancellation-free formulas for the
expansions of nonzero subdeterminants.
