  We study strongly interacting ultracold spin-1/2 fermions in a honeycomb
lattice in the presence of a harmonic trap. Tuning the strength of the harmonic
trap we show that it is possible to confine the fermions in artificial
structures reminiscent of graphene nanoflakes in solid state. The confinement
on small structures induces magnetic effects which are absent in a large
graphene sheet. Increasing the strength of the harmonic potential we are able
to induce different magnetic states, such as a N\'eel-like antiferromagnetic or
ferromagnetic states, as well as mixtures of these basic states. The
realization of different magnetic patterns is associated with the terminations
of the artificial structures, in turn controlled by the confining potential.
