We present a general method to characterize the quantum correlations obtained after local measurements on multipartite systems. Sufficient conditions for a quantum system to be fully-nonlocal according to a given partition, as well as being (genuinel
y) multipartite fully-nonlocal, are derived. These conditions allow us to identify all completely-connected graph states as multipartite fully-nonlocal quantum states. Moreover, we show that this feature can also be observed in mixed states: the tensor product of five copies of the Smolin state, a biseparable and bound entangled state, is multipartite fully-nonlocal.
