Metcalfe's Law is the claim that the value of a network scales as the square of the number of people in that network. I believe this to be a grotesque overestimate, and a couple of years ago came up with a heuristic argument that not only was it an overestimate, but n log(n) was a much more reasonable estimate.
I wound up sending that as a brief note to Andrew Odlyzko, a fairly well-known researcher who discusses (among other things) the economics of networks. (Content is Not King and The many paradoxes of broadband are two of his papers relating to networks.)
We had a brief discussion and I forgot all about it. Until he came back to me recently with the argument expanded out, and a few other arguments added in coming up with the same estimate. And then he asked me if I wanted to be a co-author with him! Rather generous, considering that he's well-known and he did all of the work...
If anyone is interested, here is the result. Constructive feedback would be appreciated if anyone has some.
