A March 13 Nature News article (Six degrees of messaging (https://web.archive.org/web/20120612094211/http://www.nature.com/news/2008/080313/full/news.2008.670.html?)) talks about a study on Microsoft Messenger chat users. Any random two Microsoft Messenger users (out of about 240 million) could be connected two each other via an average of 6 users that have chatted with each other.
This study is just another confirmation of the six degrees of separation (https://web.archive.org/web/20120612094211/http://en.wikipedia.org/wiki/Six_degrees_of_separation?) concept. A 2001 PNAS paper (https://web.archive.org/web/20120612094211/http://www.pnas.org/cgi/reprint/98/2/404.pdf?) found the same for scientific collaboration networks, using common authorship for a paper as connector. The mean distance of two random authors in the MEDLINE database was 4.6.
Based on these findings, you can almost expect the same connections through joint authorship between two random Nature Network members. Now if I could only find a tool that would help with that task. Not everybody is a mathematician and can simply calculate his Erdös number (https://web.archive.org/web/20120612094211/http://www.ams.org/mathscinet/collaborationDistance.html?) right from the American Mathematical Society website.