Erdős number

Erdos numbers are named for the Hungarian-American mathematician Paul Erdos and are an application of graph theory, a field in which he published extensively. They treat collaboration among researchers — measured by publication of joint papers — as a graph. A researcher's Erdos number is the length of the shortest path, via co-author relationships, connecting him or her to Paul Erdos. Erdos was an amazingly prolific writer with over 1500 papers in diverse areas of mathematics and over 500 collaborators.

More explicitly, it is the first number in the following list which applies to you:

• 0: You are Paul Erdos .
• 1: You have co-authored a paper with Erdos.
• 2: You have done a paper with someone of Erdos number 1.
• N+1 You have co-authored a paper with someone of Erdos number N.

If there is no chain of co-author relations connecting you to Erdos, your Erdos number is considered infinite.

Erdos number connections extend far outside mathematics.[1] In Physics, Einstein has Erdos number two while Pauli, Feynman, Born and Gell-Mann among others are at three, Dirac and Heisenberg four. For some fields a few authors with low Erdos numbers provide the main connection, for example, Ron Rivest in cryptography and John Tukey in Statistics, both with Erdos number two. Prominent people in many other fields also have finite Erdos numbers — from Piaget, Shannon, von Neumann, and both Google founders at three, to Chomsky, Popper and Bill Gates at four.

There are analogous measures in other fields. Actors calculate their Kevin Bacon number, based on appearing in films together, and Go players have a Shusaku number, the minimum number of games linking them to a great 18th century master.

The The Erdös Number Project at Oakland University in Rochester, Michigan has much more information.