  We show a dramatic deviation from ergodicity for the conductance fluctuations
in graphene. In marked contrast to the ergodicity of dirty metals, fluctuations
generated by varying magnetic field are shown to be much smaller than those
obtained when sweeping Fermi energy. They also exhibit a strongly anisotropic
response to the symmetry-breaking effects of a magnetic field, when applied
perpendicular or parallel to the graphene plane. These results reveal a complex
picture of quantum interference in graphene, whose description appears more
challenging than for conventional mesoscopic systems.
