  We compare the classification of the electron bands in graphene, obtained by
group theory algebra in the framework of tight-binding model (TBM), with that
calculated in the density-functional theory (DFT) framework. Identification in
the DFT band-structure of all eight energy bands (four valence and four
conduction bands) corresponding to the TBM-derived energy bands is performed
and corresponding analysis is presented. The four occupied (three $\sigma$- and
one $\pi$-like) and three unoccupied (two $\sigma$- and one $\pi$-like) bands
given by DFT closely correspond to those predicted by TBM, both by their
symmetry and their dispersion law. However, the two lowest lying at the
$\Gamma$-point unoccupied bands (one of them of a $\sigma$-like type and the
other of a $\pi$-like one), are not of TBM type. According both to their
symmetry and to the electron density these bands are plane waves orthogonal to
the TBM valence bands; dispersion of these states can be determined
unambiguously up to the Brillouin zone borders. On the other hand, the fourth
unoccupied band given by the TBM, can be identified among those given by the
DFT band calculations; it is situated rather high with respect to energy. The
interaction of this band with the free-electron states is so strong, that it
exists only in a part of $k$-space.
