transfer function of active filters
I can't really speak for signal flow graphs, simply because I don't use them. I've always seem them as useful for planning an algorithm in assembly, but for non discrete time signals, they're more confusing than helpful.

It is possible to extract transfer functions directly from a Sallen-Key circuit, but you need to know what you're looking for, and what the basic transfer functions look like. For example:


Here we have an assumed Sallen-Key second order low pass, where \$R=R_1=R_2,\ C=C_1=C_2\$. The generic transfer function is known, as well as \$\alpha=3-\dfrac{R_4}{R_3}\$, and \$\omega_c=\dfrac{1}{RC}\$. From there, it can be reconstructed.