  The affine $su(3)$ modular invariant partition functions in 2d RCFT are
associated with a set of generalized Coxeter graphs. These partition functions
fall into two classes, the block-diagonal (Type I) and the non block-diagonal
(Type II) cases, associated, from spectral properties, to the subsets of
subgroup and module graphs respectively. We introduce a modular operator
$\hat{T}$ taking values on the set of vertices of the subgroup graphs. It
allows us to obtain easily the associated Type I partition functions. We also
show that all Type II partition functions are obtained by the action of
suitable twists $\vartheta$ on the set of vertices of the subgroup graphs.
These twists have to preserve the values of the modular operator $\hat{T}$.
