Reed's law

Reed's law is the assertion of David P. Reed that the utility of large , particularly social networks, can scale exponentially with the size of the network.

The reason for this is that the number of possible sub-groups 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, $frac\{N(N-1)\}\{2\}$ (which follows Metcalfe's law)so that even if the utility of groups available to be joined is very small on a peer-group basis, eventually the network effect of potential group membership can dominate the overall economics of the system.

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 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 $2^n$. So the value of a GFN increases exponentially, in proportion to $2^n$. I call that Reed's Law. And its implications are profound."

See also

* Coase's penguin
* Social capital
* Metcalfe's law
* Sarnoff's law
* Andrew Odlyzko's "Content is Not King"
* List of adages named after people
* List of eponymous laws

References

External links

* [http://www.reed.com/gfn/docs/reedslaw.html That Sneaky Exponential—Beyond Metcalfe's Law to the Power of Community Building]
* [http://www.contextmag.com/archives/199903/digitalstrategy.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.