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

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

## References

## External links

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.

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 $2^N$.

- "[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."

- 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

- 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.
- 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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Last updated on Friday September 19, 2008 at 14:47:08 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Friday September 19, 2008 at 14:47:08 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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