  Kenyon and Wilson showed how to test if a circular planar electrical network
with $n$ nodes is well-connected by checking the positivity of $\binom{n}{2}$
central minors of the response matrix. Their test is based on the fact that any
contiguous minor of a matrix can be expressed as a Laurent polynomial in the
central minors. Moreover, the Laurent polynomial is the generating function of
domino tilings of a weighted Aztec diamond. They conjectured that a larger
family of minors, semicontiguous minors, can also be written in terms of domino
tilings of a region on the square lattice. In this paper, we present a proof of
the conjecture.
