The first article I found was on the OR Complete blog site. There was a post that talked about tracking back articles to see who cited who, and drawing up a tree of those articles. The site also pointed to a blog post by Mike Trick, which traced back his supervisors, describing his father, grandfather etc. of his family of supervisors. He thinks that we could all be related to Newton eventually!
I’m not sure how genealogists would deal with some of the issues that this type of tree raises. As Mike points out, one of his supervisors his both his father and grandfather. I’m not quite sure if this is allowed in the non-academic world and how it would be represented.
But like your Erdos number, it would give you some idea how well you are related to the great scientists of the past.
As the OR-Complete post points out, it might also give us more insight into some of the forgotten scientists of days gone by.
In fact, and this seems to be the original motivation for Mike’s post, the Mathematics Genealogy Project has started to compile such a family tree. I found my supervisor on there, but none of my graduated students. I could do worse that starting to populate their database.