Erdős number

The shortest number of collaborations with other mathematicians through which a particular mathematician can be connected to Paul Erdős is the Erdős number of that mathematician. For example, N. J. A. Sloane coauthored Sphere Packings, Lattices and Groups with John Horton Conway. In turn, Conway coauthored a paper with Erdős in 1979, thus Sloane’s Erdős number is 2. Since Erdős died in 1996, 2 is the lowest Erdős number a mathematician working today can achieve.

One way to visualize the Erdős number is by drawing up a collaboration graph $G$ whose vertex set consists of all persons, where two vertices $x$ and $y$ are connected by an edge if and only if $x$ and $y$ have a joint publication. Then the Erdős number of a person $x$ is the distance in $G$ (possibly infinity) of $x$ from Erdős.