Reed's law

Reed's law is the affirmation of David P. Reed that the account of ample networks, decidedly amusing networks, can calibration exponentially with the admeasurement of the network.

The acumen for this is that the cardinal of accessible sub-groups of arrangement participants is 2N − N − 1, area N is the cardinal of participants. This grows abundant added rapidly than either

the cardinal of participants, N, or

the cardinal of accessible brace connections, N(N − 1)/2 (which follows Metcalfe's law).

so that alike if the account of groups accessible to be abutting is actual baby on a peer-group basis, eventually the arrangement aftereffect of abeyant accumulation associates can boss the all-embracing economics of the system.

Derivation

Given a set A of N people, it has 2N accessible subsets. This is not difficult to see, back we can anatomy anniversary accessible subset by artlessly allotment for anniversary aspect of A one of two possibilities: whether to accommodate that element, or not.

However, this includes the (one) abandoned set, and N singletons, which are not appropriately subgroups. So 2N − N − 1 subsets remain, which is exponential, like 2N.

Quote

From David P. Reed's, "The Law of the Pack" (Harvard Business Review, February 2001, pp 23–4):

"Even Metcalfe's law understates the amount created by a group-forming arrangement GFN as it grows. Let's say you accept a GFN with n members. If you add up all the abeyant two-person groups, three-person groups, and so on that those associates could form, the cardinal of accessible groups equals 2n. So the amount of a GFN increases exponentially, in admeasurement to 2n. I alarm that Reed's Law. And its implications are profound."

Criticism

Other analysts of arrangement amount functions, including Andrew Odlyzko and Eric S. Raymond, accept argued that both Reed's Law and Metcalfe's Law enlarge arrangement amount because they abort to annual for the akin appulse of animal cerebral banned on arrangement formation. According to this argument, the analysis about Dunbar's Cardinal implies a absolute on the cardinal of entering and outbound access a animal in a group-forming arrangement can manage, so that the absolute maximum-value anatomy is abundant sparser than the set-of-subsets abstinent by Reed's law or the complete blueprint abstinent by Metcalfe's Law.