  We prove an upper bound for the evaluation of all classical SU(2) spin
networks conjectured by Garoufalidis and van der Veen. This implies one half of
the analogue of the volume conjecture which they proposed for classical spin
networks. We are also able to obtain the other half, namely, an exact
determination of the spectral radius, for the special class of generalized drum
graphs. Our proof uses a version of Feynman diagram calculus which we developed
as a tool for the interpretation of the symbolic method of classical invariant
theory, in a manner which is rigorous yet true to the spirit of the classical
literature.
