Your assumption, that there are non-stop flights connecting every "hub" (by whatever definition) to every other hub, is flawed. This may be true within a limited area such as Europe or the U.S., but is not true on a worldwide basis. As one example with which I'm personally familiar, there are no non-stop flights between BOS (Boston, Mass.; the hub for New England regional flights) and SCL (Santiago, Chile; the hub of that country). Therefore, travel between (for example) MVY (Martha's Vineyard, Mass.) and PUQ (Punta Arenas, Chile) requires a minimum of three connections: at BOS, at an intermediate hub such as MIA, and at SCL.

I wouldn't be surprised if there are origin-destination pairs that require a minimum of four connections, though I can't think of any at the moment.