  We study the Bose-Einstein condensate in a honeycomb optical lattice within
Bogoliubov theory and find that for a ${\bf k} = 0$ condensate, the Dirac
points appear in the Bogoliubov excitation spectrum when $0 < \beta < 2$, which
illustrates that the bose-bose interaction does not change the Dirac point
structure but only give a modification of the velocity of the Dirac cone. When
the bosons are driven to condense at ${\bf k} = {\bf K}$, however, we find that
the topology of the Dirac points will be altered by arbitrary weak interaction.
Furthermore, we find that the next-nearest-neighbor hopping in an isotropic and
an anisotropic lattice has different effects to the dynamics of the condensate
and it should be taken into account when the lattice is not sufficiently deep.
