  We prove statement conjectured in [Baez and Barrett:2001] that every
3-edge-connected SL(2,C) spin-network with invariants of certain class is
integrable. It means that the regularized evaluation (defined by a suitable
integral) of such a spin-network is finite. Our proof is quite general. It is
valid for relativistic spin-networks of Barrett and Crane as well as for
spin-networks with the Engle-Pereira-Rovelli-Livine intertwiners and for some
generalization of both. The result interesting from the group representation
point of view opens also a possibility of defining vertex amplitudes for
Spin-Foam models based on non-simplicial decompositions.
