  The electromagnetic response of graphene, expressed by the dielectric
function, and the spectrum of collective excitations are studied as a function
of wave vector and frequency. Our calculation is based on the full band
structure, calculated within the tight-binding approximation. As a result, we
find plasmons whose dispersion is similar to that obtained in the single-valley
approximation by Dirac fermions. In contrast to the latter, however, we find a
stronger damping of the plasmon modes due to inter-band absorption. Our
calculation also reveals effects due to deviations from the linear Dirac
spectrum as we increase the Fermi energy, indicating an anisotropic behavior
with respect to the wave vector of the external electromagnetic field.
