Discover

'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, (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.

Contents

Derivation

Quote

See also

External links

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 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

★ Andrew Odlyzko's "Content is Not King"

★ List of adages named after people

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.

★ 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.