  Motivated by recent experimental observations of size quantization of
electron energy levels in graphene quantum dots \cite{ponomarenko} we
investigate the level statistics in the simplest tight-binding model for
different dot shapes by computer simulation. The results are in a reasonable
agreement with the experiment which confirms qualitatively interpretation of
observed level statistics in terms of "Dirac billiards" without taking into
account many-body effects. It is shown that edge effects are in general
sufficient to produce the observed level distribution and that even strong bulk
disorder does not change the results drastically.
