  Mean-field Bloch bands of a Bose-Einstein condensate in a honeycomb optical
lattice are computed. We find that the topological structure of the Bloch bands
at the Dirac point is changed completely by the atomic interaction of arbitrary
small strength: the Dirac point is extended into a closed curve and an
intersecting tube structure arises around the original Dirac point. These tubed
Bloch bands are caused by the superfluidity of the system. Furthermore, they
imply the inadequacy of the tight-binding model to describe an interacting
Boson system around the Dirac point and the breakdown of adiabaticity by
interaction of arbitrary small strength.
