  The graphical calculus method is generalized to study the relation between
covariant and canonical dynamics of loop quantum gravity. On one hand, a
graphical derivation of the partition function of the generalized Euclidean
Engle-Pereira-Rovelli-Livine (EPRL) spin-foam model is presented. On the other
hand, the action of a Euclidean Hamiltonian constraint operator on certain spin
network states is calculated by graphical method. It turns out that the EPRL
model can provide a rigging map such that the Hamiltonian constraint operator
is weakly satisfied on certain physical states for the Immirzi parameter
$\beta=1$. In this sense, the quantum dynamics between the covariant and
canonical formulations are consistent to each other.
