Reed's law is the assertion of David P. Reed that the utility of large networks, particularly social networks, can scale exponentially with the size of the network.
The reason for this is that the number of possible subgroups of network participants is 2^{N} − N − 1, where N is the number of participants. This grows much more rapidly than either

the number of participants, N, or

the number of possible pair connections, N(N − 1)/2 (which follows Metcalfe's law).
so that even if the utility of groups available to be joined is very small on a peergroup basis, eventually the network effect of potential group membership can dominate the overall economics of the system.
Contents

Derivation 1

Quote 2

Criticism 3

See also 4

References 5

External links 6
Derivation
Given a set A of N people, it has 2^{N} possible subsets. This is not difficult to see, since we can form each possible subset by simply choosing for each element of A one of two possibilities: whether to include that element, or not.
However, this includes the (one) empty set, and N singletons, which are not properly subgroups. So 2^{N} − N − 1 subsets remain, which is exponential, like 2^{N}.
Quote
From David P. Reed's, "The Law of the Pack" (Harvard Business Review, February 2001, pp 23–4):

"[E]ven Metcalfe's law understates the value created by a groupforming network [GFN] as it grows. Let's say you have a GFN with n members. If you add up all the potential twoperson groups, threeperson groups, and so on that those members could form, the number of possible groups equals 2^{n}. So the value of a GFN increases exponentially, in proportion to 2^{n}. I call that Reed's Law. And its implications are profound."
Criticism
Other analysts of network value functions, including Andrew Odlyzko and Eric S. Raymond, have argued that both Reed's Law and Metcalfe's Law overstate network value because they fail to account for the restrictive impact of human cognitive limits on network formation. According to this argument, the research around Dunbar's Number implies a limit on the number of inbound and outbound connections a human in a groupforming network can manage, so that the actual maximumvalue structure is much sparser than the setofsubsets measured by Reed's law or the complete graph measured by Metcalfe's Law.
See also
References
External links

That Sneaky Exponential—Beyond Metcalfe's Law to the Power of Community Building

Weapon of Math Destruction: A simple formula explains why the Internet is wreaking havoc on business models.

KKlaw for Group Forming Services, XVth International Symposium on Services and Local Access, Edinburgh, March 2004, presents an alternative way to model the effect of social networks.
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