[ed: Links ours. Also, 2^n = "2 to the power of n"; as in 2^3 = 8, 2^4 = 16. Included here as "groups" are the one-person "groups" and the empty set.]
I'll let Reed somewhat arrogantly claim the name on this law. It's simply the size of the power set of users, but he's right that this is a more powerful concept than MetcalfesLaw taken by itself. With MetcalfesLaw, there is still some external force, like an instant messaging system, constructing the network. With ReedsLaw, the users themselves construct their network. This added flexibility to the users increases the number of CommunicationChannels available.
Anyone comparing the value of a
Perhaps his numbers are nonsense, but he's right about there being some additional value in the subgroups. Not all of the subgroups, but some of them. As an online community grows, the subgroup value may come to dominate.
This may have happened to WardsWiki. Eg there would seem to be a films subgroup. Films are off-topic (that is, they're nothing to do with programming), but a fraction of any group of programmers are also interested in films and if you make the main group large enough, the subgroup attains critical mass. In the case of WhyClublet and MeatBall, the subgroups eventually calved off and became independent communities.
According to ReedsLaw, this calving off may be a bad thing. It reduces N; it dilutes the user base and makes it harder for subgroups to form. For example, the films subgroup will have been split into 3 parts by the WhyClublet/MeatBall/Wiki separation, and each part may be too small to attain critical mass. So some possible value is lost.
Here is the anti-reductionism law:
Every attempt to capture a human-interaction phenomena by just one number, however smartly derived, is doomed to failure
There is a strong critique of the application of both Metcalfe's and Reed's laws by Andrew Odlyzko, B. Briscoe and B. Tilly. For Reed, although 2 to the nth power potential groups can be formed from a network of of size n, in practice this never happens. Not all of the potential subsets/subgroups get made. Similarly, for Metcalfe, there are good arguments that a more accurate relation is not (n squared), but something approaching n*(log n). See "A refutation of Metcalfe's Law and a better estimate for the value of networks and network interconnections" at [Andrew Odlyzko's bibliography]. -- MarkJones