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What is 6 degree of separation?

What is 6 degree of separation?
It refers to the idea that everyone is on average approximately six steps away, by way of introduction, from any other person on Earth, so that a chain of, "a friend of a friend" statements can be made, on average, to connect any two people in six steps or fewer. It was originally set out by Frigyes Karinthy and popularized by a play written by John Guare.

In the 1960s, Stanley Milgram of Harvard used packages as his research medium in a famous experiment in social connections. He sent packages to volunteers in the Midwest, instructing them to get the packages to strangers in Boston, but not directly; participants could mail a package only to someone they knew. The average number of times a package changed hands was remarkably few, about six. It was a classic demonstration of the “small-world phenomenon,” captured in the popular phrase “six degrees of separation.”

In 2001, Duncan Watts, a professor at Columbia University, attempted to recreate Milgram's experiment on the Internet, using an e-mail message as the "package" that needed to be delivered, with 48,000 senders and 19 targets (in 157 countries). Watts found that the average (though not maximum) number of intermediaries was around six.

A 2007 study by Jure Leskovec and Eric Horvitz examined a data set of instant messages composed of 30 billion conversations among 240 million people. They found the average path length among Microsoft Messenger users to be 6.6 (some now call the theory, " seven degrees of separation" because of this).

Mathematicians use an analogous notion of collaboration distance: two persons are linked if they are coauthors of an article. The collaboration distance with mathematician Paul Erdős is called the Erdős number.

The idea of the Erdős number was created by friends as a humorous tribute to the enormous output of Erdős, one of the most prolific modern writers of mathematical papers, and has become well known in scientific circles as a tongue-in-cheek measurement of mathematical prominence.

Paul Erdős was an influential and itinerant mathematician, who spent a large portion of his later life living out of a suitcase and writing papers with those of his colleagues willing to give him room and board. He published more papers during his life (at least 1,525) than any other mathematician in history.

To find out Erdős number, you can go to the following link, type your name in the order: lastname, first name find out Erdős number then it will pump out all the co-authors to link to Paul Erdos.

For example, there is a famous mathematician, youngest full professor ever in US, Terrence Tao, his Erdos number is 2:

Terence C. Tao coauthored with Vitaly Bergelson by MR2594614(2011b:37009)
Vitaly Bergelson coauthored with Paul Erdős by MR1425184 (97i:11007)

Another one, famous Russian mathematician, Grigori Perelman, Feilds' medalist, his Erdos number is 4, it's possibly because he didn't write many papers, not co-author with many other mathematicians either.

Some Asian professor, his Erdos number is 3:

Qi S. Zhang coauthored with Zhong Xin Zhao MR1458274 (98j:35093)
Zhong Xin Zhao coauthored with Kai Lai Chung MR0709862 (85i:60068)
Kai Lai Chung coauthored with Paul Erdős MR0023010 (9,292f)

Those Erdos numbers might not be correct, it only gives one connection, but not the connection with the least path. So your Erdos number could be less.

There are a number of variations on the concept have been proposed to apply to other fields. For instance, in Physics, there is Einstein number; in Acting, there is Bacon number; in Chess area, there is Morphy number etc.