Paul Erdős was the great peripatetic, and highly prolific, mathematician of the 20th century. A terrific web page run by Jerry Grossman at Oakland University provides details of the Erdős Project. Erdős was a pioneer in graph theory, which provides the formal tools for the analysis of social networks. A collaboration graph is a special graph in which the nodes are authors and an edge connects authors if they co-author a publication. Erdős was such a prolific collaborator that he forms a major hub in the mathematics collaboration graph, linking many disparate authors in the different realms of pure and applied mathematics.
For whatever reason, today I used Grossman's directions for finding one's number. <drum roll> My Erdős number is 4. The path that leads me to Erdős is pretty sweet, I have to say. This past year, I published a paper in PNAS with Marc Feldman. Marc wrote a number of papers (here's one) with Sam Karlin (who, I'm proud to say, came and slept through at least one talk I gave at the Morrison Institute). Karlin wrote a paper with Gábor Szegő, who wrote a paper with Erdős. Lots of Stanford greatness there that I feel privileged to be a part of. It turns out that I have independent (though longer) paths through my co-authors Marcel Salathé and Mark Handcock as well.