  We investigate the non-local properties of graph states. To this aim, we
derive a family of Bell inequalities which require three measurement settings
for each party and are maximally violated by graph states. In turn, for each
graph state there is an inequality maximally violated only by that state. We
show that for certain types of graph states the violation of these inequalities
increases exponentially with the number of qubits. We also discuss connections
to other entanglement properties such as the positivity of the partial
transpose or the geometric measure of entanglement.
