Devdas Bhagat has a nice observation about the "value of the network". The question he was answering is in italics
Seen from this perspective, the value of the network probably would be between n to the power 1.414 (square root of 2) and 1.732 (square root of 3).
I would say that it does grow a bit faster than that. Also, as people learn to use the network better, they create value that the original designers of the network never dreamt of. That act of creation drives up the value of the network even more.