  Many experiments in quantum information aim at creating graph states.
Quantifying the purity of an experimentally achieved graph state could in
principle be accomplished using full-state tomography. This method requires a
number of measurement settings growing exponentially with the number of
constituents involved. Thus, full-state tomography becomes experimentally
infeasible even for a moderate number of qubits.
  In this paper we present a method to estimate the purity of experimentally
achieved graph states with simple measurements. The observables we consider are
the stabilizers of the underlying graph. Then, we formulate the problem as:
"What is the state with the least purity that is compatible with the
measurement data?" We solve this problem analytically and compare the obtained
bounds with results from full-state tomography for simulated data.
