Editing Reed's law

{{short description|Network value increases as 2^n, this being the number of possible subgroups within the network}}
'''Reed's law''' is the assertion of [[David P. Reed]] that the [[utility]] of large [[wiktionary:Network|networks]], particularly [[social network]]s, can [[exponential growth|scale exponentially]] with the size of the network.<ref>{{cite web |title=Understand and Obey the Laws of Networking: Ignorance of the laws of networking is no excuse |first=Scott |last=Hogg |work=Network World |date=October 5, 2013 |url= https://www.networkworld.com/article/746622/cisco-subnet-understand-and-obey-the-laws-of-networking.html |access-date=November 2, 2017}}</ref>

The reason for this is that the number of possible sub-groups of network participants is 2<sup>''N''</sup>&nbsp;&minus;&nbsp;''N''&nbsp;&minus;&nbsp;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''&nbsp;&minus;&nbsp;1)/2 (which follows [[Metcalfe's law]]).
so that even if the utility of groups available to be joined is very small on a per-group basis, eventually the [[network effect]] of potential group membership can dominate the overall economics of the system.

==Derivation==
Given a [[Set (mathematics)|set]] ''A'' of ''N'' people, it has 2<sup>''N''</sup> 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'' [[Singleton (mathematics)|singletons]], which are not properly subgroups. So 2<sup>''N''</sup>&nbsp;&minus;&nbsp;''N''&nbsp;&minus;&nbsp;1 subsets remain, which is exponential, like&nbsp;2<sup>''N''</sup>.

==Quote==
From David P. Reed's, "The Law of the Pack" (Harvard Business Review, February 2001, pp 23–4):<!--Not a proper reference citation; please use.<ref name"SomethingUniqueHere">{{Cite book|...}}</ref>-->

:"[E]ven Metcalfe's law understates the value created by a group-forming network [GFN] as it grows. Let's say you have a GFN with ''n'' members. If you add up all the potential two-person groups, three-person groups, and so on that those members could form, the number of possible groups equals 2<sup>''n''</sup>. So the value of a GFN increases exponentially, in proportion to&nbsp;2<sup>''n''</sup>. I call that Reed's Law. And its implications are profound."

== Business implications ==
Reed's Law is often mentioned when explaining competitive dynamics of internet platforms. As the law states that a network becomes more valuable when people can easily form subgroups to collaborate, while this value increases exponentially with the number of connections, business platform that reaches a sufficient number of members can generate [[network effect]]s that dominate the overall economics of the system.<ref>{{Cite news|url=https://www.networkworld.com/article/956104/the-network-effect-on-wealth-creation.html|title=The network effect on wealth creation|last=Heckart|first=Christine|work=Network World|access-date=2017-11-07|language=en}}</ref>

==Criticism==

Other analysts of network value functions, including [[Andrew Odlyzko]], have argued that both Reed's Law and Metcalfe's Law <ref>{{Cite news|url=https://spectrum.ieee.org/metcalfes-law-is-wrong|title=Metcalfe's Law is Wrong|work=IEEE Spectrum: Technology, Engineering, and Science News|access-date=2017-11-10|language=en}}</ref> 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 group-forming network can manage, so that the actual maximum-value structure is much sparser than the set-of-subsets measured by Reed's law or the complete graph measured by Metcalfe's law.

== See also ==
* [[Andrew Odlyzko]]'s "Content is Not King"
* [[Beckstrom's law]]
* [[Coase's penguin]]
* [[List of eponymous laws]]
* [[Metcalfe's law]]
* [[Six Degrees of Kevin Bacon]]
* [[Sarnoff's law]]
* [[Social capital]]

==References==
{{reflist}}

==External links==
* [http://www.deepplum.com/dpr/locus/gfn/reedslaw.html That Sneaky Exponential&mdash;Beyond Metcalfe's Law to the Power of Community Building]
* [https://web.archive.org/web/20071008165706/http://www.contextmag.com/setFrameRedirect.asp?src=%2Farchives%2F199903%2Fdigitalstrategy.asp Weapon of Math Destruction: A simple formula explains why the Internet is wreaking havoc on business models.]
* [http://kotisivukone.fi/files/50ajatelmaa.ajatukset.fi/tiedostot/Others/kilkki_kk-law.pdf KK-law 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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