Six Degrees of Separation

"Six degrees of separation" is the theory that everyone is six or fewer steps away, by way of introduction, from any other person in the world, so that a chain of "a friend of a friend" statements can be made to connect any two people in a maximum of six steps. This theory was originally proposed by Frigyes Karinthy in 1929, and later popularized by a play of the same name by John Guare in 1990. As one of the characters states:

"I read somewhere that everybody on this planet is separated by only six other people.
Six degrees of separation between us and everyone else on this planet. The President of the
United States, a gondolier in Venice, just fill in the names. I find it A) extremely 
comforting that we're so close, and B) like Chinese water torture that we're so close 
because you have to find the right six people to make the right connection... I am bound to 
everyone on this planet by a trail of six people."

- Ouisa Kittredge, a character in the play "Six Degrees of Separation"

A more recognizable application of the theory finds itself in the game "Six Degrees of Kevin Bacon", where the goal is to link any actor to Kevin Bacon through no more than six connections, where two actors are connected if they have appeared in a movie or commercial together.

The field of mathematics has its own version of the game, defined by the Erdos number of a mathematician. Here, two persons are linked if they are coauthors of an article. The length of the shortest chain linking a someone and the prolific mathematician Paul Erdos is then the aforementioned Erdos number.

In a random network, Duncan J. Watts and Steven Strogatz showed that the average path length between two nodes is equal to $\ln N / \ln K$, where $N$ is the total number of nodes, and $K$ is the number of acquaintances per node.

As specific examples, in 2011 the average distance was 4.74 on Facebook, and on Twitter the average distance is 4.67.