  We analyze the collective gravitational interaction among gas clouds in the
inner regions of galactic disks and find that it leads to accretion at a rate
$\sim M_{mc}\Omega (M_{mc}/M_t)^2$; where $M_{mc}$ is the molecular mass of the
disk, $M_t$ is sum of the central plus any axisymmetrically distributed mass,
and $\Omega$ is the mean angular speed of clumps. We discuss applications of
this result to the mega-maser galaxy NGC 4258, for which we have observational
evidence that the maser spots are concentrated in a thin molecular disk which
is clumpy, and find the accretion rate to be about $1.5\times 10^{-3}$ solar
mass per year. If the gravitational energy release of this inward falling gas
were to be radiated away efficiently, then the resulting luminosity would
greatly exceed the observed central luminosity of NGC 4258, indicating that
most of the thermal energy of the gas is advected with the flow into the
blackhole as proposed by Lasota et al. (1996).
  The gravitational interactions among molecular clouds lying within the inner
kpc of our galaxy give an accretion rate of about $10^{-5}$ solar mass per
year, which is consistent with the value obtained by Narayan et al. (1995) by
fitting the spectrum of Sagitarrius A$^*$. We also discuss possible application
of this work to quasar evolution.
