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.
The reason for this is that the number of possible sub-groups of network participants is , where is the number of participants. This grows much more rapidly than either
- the number of participants, , 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 peer-group basis, eventually the network effect of potential group membership can dominate the overall economics of the system.
Given a set A
people, it has
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 subsets remain, which is exponential, like .
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 . So the value of a GFN increases exponentially, in proportion to . I call that Reed's Law. And its implications are profound."