  Network connectivity is usually addressed for convex domains where a direct
line of sight exists between any two transmitting/receiving nodes. Here, we
develop a general theory for the network connectivity properties across a small
opening, rendering the domain essentially non-convex. Our analytic approach can
go only so far as we encounter what is referred to in statistical physics as
quenched disorder making the problem non-trivial. We confirm our theory through
computer simulations, obtain leading order approximations and discuss possible
extensions and applications.
