  In the framework of quantum field theory, a graviton interacts locally with a
quantum state having definite mass, i.e. the gravitational mass eigenstate,
while a weak boson interacts with a state having definite flavor, i.e. the
flavor eigenstate. An interaction of a neutrino with an energetic graviton may
trigger the collapse of the neutrino to a definite mass eigenstate with
probability expressed in terms of PMNS mixing matrix elements. Thus, gravitons
would induce quantum decoherence of a coherent neutrino flavor state similarly
to how weak bosons induce quantum decoherence of a neutrino in a definite mass
state. We demonstrate that such an essentially quantum gravity effect may have
strong consequences for neutrino oscillation phenomena in astrophysics due to
relatively large scattering cross sections of relativistic neutrinos undergoing
large-angle radiation of energetic gravitons in gravitational field of a
classical massive source (i.e. the quasi-classical case of gravitational
Bethe-Heitler scattering). This graviton-induced {\it decoherence} is compared
to {\it decoherence} due to propagation in the presence of the Earth matter
effect. Based on this study, we propose a new technique for the indirect
detection of energetic gravitons by measuring the flavor composition of
astrophysical neutrinos.
