  Although Potent purports to use only radial velocities in reconstructing the
potential velocity field of galaxies, the derivation of transverse components
is implicit in the smoothing procedures adopted. Thus the possibility arises of
using nonradial line integrals to derive a smoothed velocity field. For an
inhomogeneous galaxy distribution the optimal path for integration need not be
radial, and can be obtained using max-flow algorithms. In this paper we
describe how one may use Dijkstra's algorithm to obtain this optimal path and
velocity field, and present the results of applying the algorithm to a
realistic spatial distribution of galaxies. These results show that the method
has limited effect due to the large smoothing scales employed in Potent.
However, the viability of the technique is demonstrated and, finally, we
discuss other possible methods involving averaging over an ensemble of
non-radial paths for improving a potential velocity field derived from
redshifts.

Astrophysics