Has the "six degrees of separation" theory been mathematically proven?

Question

Have scientists/professors/mathmaticians studied this theory? Does it have any legitimacy or is it just urban legend? Please include links.

Answer 1

It can't be proven rigorously, because its underpinnings are certain assumptions about how many people each person knows, and how evenly distributed those links are.

The Wikipedia article discusses the math behind it:
http://en.wikipedia.org/wiki/Six_degrees_of_separation
... but it is the assumptions underlying the math, indicate that it is possible even in a small population to have no connections between two groups:

"If the population is split in two groups of 8, perhaps by geographic boundaries, then it would be impossible to 'know' the entire population or have a connection between all individuals."

It's pretty certain that you are connected to a very large number of people by six degrees of separation. But are you connected to absolutely everyone on the planet in that manner? And is the same true of the most isolated person in the most isolated tribe in South America?

Both seem unlikely to me, and the technical articles on the topic (some referenced in the Wikipedia article) don't contain a clinching case to the contrary.

A famous experiment, discussed on the related "Small World Phenomenon" Wikipedia entry:
http://en.wikipedia.org/wiki/Small_world_phenomenon
... found six as the AVERAGE separation between people IN THE UNITED STATES (meaning that a number were longer than six, and worldwide might be even longer yet, since geographic proximity is significant).

The "Small World" Wiki entry also notes: "It is impossible for the entire human population to be acquainted within six degrees of separation because of the existence of certain populations which have had no contact with people outside their own culture, such as the Sentinelese people of North Sentinel Island."

And it references this article:
http://www.uaf.edu/northern/big_world.html
... which criticizes Milgram's work and calls the six degrees claim "the academic equivalent of an urban myth."

Answer 2

No. It was just a guess---on average. But the link below tells of a Facebook group that might help proove or disproove it.