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 himself has Erdos number zero. Anyone who is not Erdos but co-authored a paper with him has Erdos number one. In general, if researcher R has co-authors on some papers and some of those have Erdos connections to Erdos, then R's Erdos number is the lowest of the collaborator's numbers, plus one. If there is no chain connecting him or her to Erdos, R's Erdos number is considered infinite.

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.