  In this paper we study the construction of holomorphic gauge invariant
operators for general quiver gauge theories with flavour symmetries. Using a
characterisation of the gauge invariants in terms of equivalence classes
generated by permutation actions, along with representation theory results in
symmetric groups and unitary groups, we give a diagonal basis for the 2-point
functions of holomorphic and anti-holomorphic operators. This involves a
generalisation of the previously constructed Quiver Restricted Schur operators
to the flavoured case. The 3-point functions are derived and shown to be given
in terms of networks of symmetric group branching coefficients. The networks
are constructed through cutting and gluing operations on the quivers.
