  Coronal magnetic field may be characterized by how its field lines
interconnect regions of opposing photospheric flux -- its connectivity.
Connectivity can be quantified as the net flux connecting pairs of opposing
regions, once such regions are identified. One existing algorithm will
partition a typical active region into a number of unipolar regions ranging
from a few dozen to a few hundred, depending on algorithmic parameters. This
work explores how the properties of the partitions depend on some algorithmic
parameters, and how connectivity depends on the coarseness of partitioning for
one particular active region magnetogram. We find the number of connections
among them scales with the number of regions even as the number of possible
connections scales with its square.
  There are several methods of generating a coronal field, even a potential
field. The field may be computed inside conducting boundaries or over an
infinite half-space. For computation of connectivity, the unipolar regions may
be replaced by point sources or the exact magnetogram may be used as a lower
boundary condition. Our investigation shows that the connectivities from these
various fields differ only slightly -- no more than 15%. The greatest
difference is between fields within conducting walls and those in the
half-space. Their connectivities grow more different as finer partitioning
creates more source regions. This also gives a quantitative means of
establishing how far away conducting boundaries must be placed in order not to
significantly affect the extrapolation. For identical outer boundaries, the use
of point sources instead of the exact magnetogram makes a smaller difference in
connectivity: typically 6% independent of the number of source regions.
