  In this paper, we study the probability that a dense network confined within
a given geometry is fully connected. We employ a cluster expansion approach
often used in statistical physics to analyze the effects that the boundaries of
the geometry have on connectivity. To maximize practicality and applicability,
we adopt four important point-to-point link models based on outage probability
in our analysis: single-input single-output (SISO), single-input
multiple-output (SIMO), multiple-input single-output (MISO), and multiple-input
multiple-output (MIMO). Furthermore, we derive diversity and power scaling laws
that dictate how boundary effects can be mitigated (to leading order) in
confined dense networks for each of these models. Finally, in order to
demonstrate the versatility of our theory, we analyze boundary effects for
dense networks comprising MIMO point-to-point links confined within a right
prism, a polyhedron that accurately models many geometries that can be found in
practice. We provide numerical results for this example, which verify our
analytical results.
