Mostly, if an airport, however minor, has scheduled service, it will be to another airport with more services and so one can connect through to any airport in the world. E.g. one can fly from ISC - Isles of Scilly to NQY - Newquay to LHR to anywhere else.
But is there a pair or set of airports where this doesn't hold, creating an "island" of unconnected air transport?
(Fixed wing or I guess helicopter).