  Recently LIGO collaboration discovered gravitational waves \cite{Abbott_16}
predicted 100 years ago by A. Einstein. Moreover, in the key paper reporting
about the discovery, the joint LIGO \& VIRGO team presented an upper limit on
graviton mass such as $m_g < 1.2 \times 10^{-22} eV$ (Abbott et al. (LIGO
collaboration) PRL 116 (2016) 061102). Since the graviton mass limit is so
small the authors concluded that their observational data do not show
violations of classical general relativity. We consider another opportunity to
evaluate a graviton mass from phenomenological consequences of massive gravity
and show that an analysis of bright star trajectories could bound graviton mass
with a comparable accuracy with accuracies reached with gravitational wave
interferometers and expected with forthcoming pulsar timing observations for
gravitational wave detection. It gives an opportunity to treat observations of
bright stars near the Galactic Center as a wonderful tool not only for an
evaluation specific parameters of the black hole but also to obtain constraints
on the fundamental gravity law such as a modifications of Newton gravity law in
a weak field approximation. In particular, we obtain bounds on a graviton mass
based on a potential reconstruction at the Galactic Center.
