The Metcalfe Law paper is interesting, but Figure 1 is seriously flawed. There is no point at which 2 to the n = n squared = n log n = n.

He's simply renormalized around that particular point. There are coefficients implicit in each of those equations even though aren't explicitly shown.

Metcalfe's Law has always been understood to mean "the theoretical potential value", since a very large number of the links between nodes will never be made.

This same idea can be applied to Reed's Law, which states that the potential value of social networks, i.e., those with self-organizing groups, grows as 2^N (actually, 2^N - N - 1). In reality, of course, this never even comes close, because real groups don't usually organize like that ("let's make a sub-group within our group that excludes one person", etc.).

Also, virtual groups, in particular, don't tend to break off into ad hoc sub-groups if they don't have the tools to do so, e.g., the participants in one thread don't typically say "Let's go create a new group to discuss this." It's theoretically possible, but only occasionally occurs. Of course, the participants in a particular thread can be considered a sort of ad hoc sub-group, in which case you might achieve something closer to the potential, but still...

Interesting stuff - thanks for the link.