Reed's law: Difference between revisions

The reason for this is that the number of possible sub-groups of network participants is 2<mathsup>2^''N - N - 1 \, ''</mathsup>&nbsp;&minus;&nbsp;''N''&nbsp;&minus;&nbsp;1, where <math>''N</math>'' is the number of participants. This grows much more rapidly than either

* the number of participants, <math>''N</math>'', or

* the number of possible pair connections, <math>\frac{''N''(''N-''&nbsp;&minus;&nbsp;1)}{2}</math>2 (which follows [[Metcalfe's law]]).

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

From David P. Reed's, "The Law of the Pack" (Harvard Business Review, February 2001, pp 23-423–4):<!--Not a proper reference citation; please use <ref name"SomethingUniqueHere">{{Cite book|...}}</ref>.-->

:"[E]ven Metcalfe's Lawlaw 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<mathsup>2^''n''</mathsup>. So the value of a GFN increases exponentially, in proportion to &nbsp;2<mathsup>2^''n''</mathsup>. I call that Reed's Law. And its implications are profound."

* [[Beckstrom's_law |Beckstrom's Lawlaw]]