QUESTION: How can I compute the sub-groups of nodes that can communicate based on signal strength and print the lists? I don't necessarily need to know "full adjacencies"; rather, just like the example above, if 1-2 and 2-3, then 1,2,3 are in a "group".

What you want is called a Transitive Closure, which is a well known problem from graph theory. There are simple algorithms that run in cubic time worst case, but IIRC, an n^2.5 algorithm exists as well. Search on CPAN for "Graph" and "Transitive Closure" should give you a few pointers.