We discuss a renormalization procedure for random tensor networks, and show
that the corresponding renormalization-group flow is given by the Hamiltonian
vector flow of the canonical tensor model, which is a discretized model of
quantum gravity. The result is the generalization of the previous one
concerning the relation between the Ising model on random networks and the
canonical tensor model with N=2. We also prove a general theorem which relates
discontinuity of the renormalization-group flow and the phase transitions of
random tensor networks.Comment: 23 pages, 5 figures; Comments on first order transitions and
discontinuity of RG added, and minor correction
