  Colloids can acquire a dipolar interaction in the presence of an external
electric field. At high field strength, the particles form strings in the field
direction. However at weaker field strength, competition with isotropic
interactions is expected. One means to investigate this interplay between
dipolar and isotropic interactions is to consider clusters of such particles.
We have therefore identified, using the GMIN basinhopping tool, a rich library
of lowest energy clusters of a dipolar colloidal system where the dipole
orientation is fixed with respect to the z-axis, and the dipole strength is
varied for m--membered clusters of 7 <= m <=13. In the regime where the
isotropic and dipolar interactions are comparable, we find elongated
polytetrahedral, octahedral and spiral clusters as well as a set of non--rigid
clusters which emerge close to the transition to strings. We further implement
a search algorithm which identifies these minimum energy clusters in bulk
systems using the topological cluster classification [J. Chem. Phys. 139 234506
(2013)]. We demonstrate this methodology with computer simulations which shows
instances of these clusters as a function of dipole strength.
