I don't know why, but the \pause
command seems to be causing troubles. If you replace
\begin{pgfonlayer}{background}
\pause
\foreach \source / \dest in {d/a,d/f,a/b,b/e,e/c,e/g}
\path<+->[selected edge] (\source.center) -- (\dest.center);
\foreach \source / \dest / \fr in {d/b/4,d/e/5,e/f/5,b/c/6,f/g/7}
\path<\fr->[ignored edge] (\source.center) -- (\dest.center);
\end{pgfonlayer}
by
\begin{pgfonlayer}{background}
\foreach \source / \dest / \fr in {d/a/2,d/f/3,a/b/4,b/e/5,e/c/6,e/g/7}
\path<\fr->[selected edge] (\source.center) -- (\dest.center);
\foreach \source / \dest / \fr in {d/b/4,d/e/5,e/f/5,b/c/6,f/g/7}
\path<\fr->[ignored edge] (\source.center) -- (\dest.center);
\end{pgfonlayer}
it works.