We formulate Yang-Mills theory in terms of the large-N limit, viewed as a
classical limit, of gauge-invariant dynamical variables, which are closely
related to Wilson loops, via deformation quantization. We obtain a Poisson
algebra of these dynamical variables corresponding to normal-ordered quantum
(at a finite value of $\hbar$) operators. Comparing with a Poisson algebra one
of us introduced in the past for Weyl-ordered quantum operators, we find, using
ideas closly related to topological graph theory, that these two Poisson
algebras are, roughly speaking, the same. More precisely speaking, there exists
an invertible Poisson morphism between them.