This is an area that has had quite a number of published analyses, and one area that's received a lot of attention is the population of movie actors/actresses, with the premise being pretty well accepted that every performer has been in a movie with another performer who was in another movie with ... etc., with the result that the population of movie performers is a closed set with 6-degree of separation paths joining every pair of performers. For this particular population, some have claimed "proofs" that even 5 degrees of separation may be sufficient; but I don't believe they're considered "rigorous" proofs.

There have been numerous arguments, however, that for "really complex populations" the six-degrees may not hold. Some have argued that the current internet (i.e. every user on every server accessible from any server that's accessible from ... etc) is a higher order population, with arguments that the maximum degree of separation may reach 13 or more. (I believe that's the highest credible estimate I've seen.) Ohers claim to be able to show it's "no more than 9." There seems to be general agreement that 6 is not enough.

The greater "separation" of the internet is due largely to many "sequestered" servers that connect to the net as a whole only via extremely narrow paths, and the analysis is complicated by how one treats members of the population who can receive but not send (i.e. "half-links") or vice-versa.

If one person in the general population is six-degrees removed from at least one other person, then the hermit/survivalist in the wilds of Idaho (a random pick) who is known only to the first person is seven-degrees removed from at least one other person - hence it's easy to see how the separation could be rapidly expanded, although the expansion past 6 would apply only if rather extreme "misfits" are included in the population.

John