  We show that every uniform state on the sphere is essentially a superposition
of regular graphs. In addition, we develop a graph-based ansatz to construct
trial FHQ ground states sharing the local properties of Jack polynomials. In
particular, our graphic states have the $(k,r)$ clustering property. Moreover,
a subclass of the construction is realizable as the densest zero-energy state
of a model that modifies the projection Hamiltonian.
