  I discuss the role played by the spin-network basis and recoupling theory (in
its graphical tangle-theoretic formulation) and their use for performing
explicit calculations in loop quantum gravity. In particular, I show that
recoupling theory allows the derivation of explicit expressions for the
eingenvalues of the quantum volume operator. An important side result of these
computations is the determination of a scalar product with respect to which
area and volume operators are symmetric, and the spin network states are
orthonormal.
