The Erdos Number is a type of measure of distance in a social network, a variant of the small world phenomenon meme “Six Degrees of Separation,” which says that any two people in the world are six or fewer acquaintances apart.

For example, you might have heard of the “Six Degrees of Kevin Bacon” game where the challenge is to find a path between anyone involved in the Hollywood movie industry and actor Kevin Bacon. The “Bacon Number” is the number of degrees of separation between a given actor and Kevin Bacon.

Consider Elvis Presley:

- Edward Asner was in JFK (1991) with Kevin Bacon.
- Elvis Presley was in Change of Habit (1969) with Edward Asner.

Kevin Bacon has a Bacon Number of 0, Ed Asner has a Bacon Number of 1, and Elvis has a Bacon Number of 2.

For mathematicians, the Erdos Number is known as the collaboration distance between an author and the prolific mathematician Paul Erdős–i.e., using collaborative research publications as the unit of distance instead of joint movie appearances.

For example, my Erdos Number is 3:

- Erdős, P.; Silverman, R.; Stein, A. Intersection properties of families containing sets of nearly the same size. Ars Combin. 15 (1983), 247–259.
- Kanungo, Tapas; Mount, David M.; Netanyahu, Nathan S.; Piatko, Christine; Silverman, Ruth; Wu, Angela Y. The analysis of a simple $k$-means clustering algorithm. Proceedings of the Sixteenth Annual Symposium on Computational Geometry (Hong Kong, 2000), 100–109 (electronic), ACM, New York, 2000.
- “Semantically Informed Machine Translation,” K. Baker, S. Bethard, M. Bloodgood, R. Brown, C. Callison-Burch, Glen Coppersmith, B. Dorr, W. Filardo, Kendall Giles, A. Irvine, M. Kayser, L. Levin, J. Martineau, J. Mayfield, S. Miller, A. Phillips, A. Philpot, Christine Piatko, L. Schwartz, D. Zajic, Technical Report No. 002, Human Language Technology Center of Excellence, Johns Hopkins University, Baltimore, Maryland, January 2010.