Erdös number

• Paul Erdös has an Erdös number of zero.
• The Erdös number of mathematician M is defined to be the minimum of the Erdös numbers of all the mathematicians that M coauthored a mathematical paper with, plus one.

The Erdos number honours the late Hungarian mathematician Paul Erdös who was one of the most prolific publishers of papers in mathematical history. He wrote around 1500 mathematical articles in his lifetime, mostly co-authored with other persons. He had about 500 collaborators, these are the people with Erdös number 1.

Erdös numbers have been a part of the folklore of mathematicians throughout the world for many years. Amongst all working mathematicians at the turn of the millennium, the numbers range up to 15, but the average is less than 5, and almost everyone with a finite Erdös number has a number less than 8.

The Bacon number is an application of the same idea to the movie industry, connecting actors that appeared in a film together.

Jerry Grossman[?], Marc Lipman[?], and Eddie Cheng have been looking at some questions in pure graph theory motivated by these collaboration graphs.

Also, Michael Barr[?] suggests "rational Erdös numbers, generalizing the idea that a person who has written p joint papers with Erdös should be assigned Erdös number 1/p. From the collaboration multigraph of the second kind (although he also has a way to deal with the case of the first kind) -- with one edge between two authors for EACH joint paper they have produced -- form an electrical network with a one-ohm resistor on each edge. The total resistance between two nodes tells how "close" these two nodes are."

• Jerry Grossman, "The Erdös number project", http://www.oakland.edu/~grossman/erdoshp. Contains statistics and a complete list of all mathematicians with an Erdös number less than or equal to 2.