  We confront a non-relativistic Bose--Einstein Condensate (BEC) model of light
bosons interacting gravitationally either through a Newtonian or a Yukawa
potential with the observed rotational curves of $12$ dwarf galaxies. The
baryonic component is modelled as an axisymmetric exponential disk and its
characteristics are derived from the surface luminosity profile of the
galaxies. The purely baryonic fit is unsatisfactory, hence a dark matter
component is clearly needed. The rotational curves of five galaxies could be
explained with high confidence level by the BEC model. For these galaxies, we
derive: (i) upper limits for the allowed graviton mass; and (ii) constraints on
a velocity-type and a density-type quantity characterizing the BEC, both being
expressed in terms of the BEC particle mass, scattering length and chemical
potential. The upper limit for the graviton mass is of the order of $10^{-26}$
$\text{eV/c}^2$, three orders of magnitude stronger than the limit derived from
recent gravitational wave detections.
