Reed's law is the assertion of David P. Reed that the utility of large networks, 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 being 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.