Gerald, I asked you a question in a comment to your answer at

http://mathoverflow.net/questions/45477/closed-form-functions-with-half-exponential-growth/45479#45479

about local solutions only to f(f(x)) = sin x around x = 0. Essentially the question is whether there is an (odd) analytic solution, i.e. nonzero radius of convergence for the formal power series solution. I screwed up, I was assuming my series would have a similar graph to one that has already been posted. That cannot happen for very long, as within the radius of convergence, should that be nonzero, the formal power series gives a genuine solution to f(f(x)) = sin x. There is a trichotomy here, given Ax, there is a functional square root given by x sqrt(A), where the case A=1 is special, so for the local analysis A >, <, = 1 matters.

I wonder if Danica McKellar looks at MO? Her Erdos number is 4, her Erdos-Bacon number is 6.
http://en.wikipedia.org/wiki/Danica_McKellar

@Cam, I disagree. In fact, I think that Erdos should be considered to have Erdos number 2 --- after all, Erdos has no joint papers with himself, although he has many joint papers with people who have joint papers with Erdos.

EDIT: Apologies to those who missed the (possibly not very funny) joke and who seemed instead to think that I was trying to reformulate the foundations of graph theory.

Random note, I deleted my comment to Gerald's MO answer and made it an MO question.

Right, the correct definition is minimum path length (as Henry slyly hinted). The minimum length of paths from Erdos to himself is 0. There are various formalizations of this which can be left as an exercise to the reader.