Reed's Law


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 2N − 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, 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 per-group basis, eventually the network effect of potential group membership can dominate the overall economics of the system.

The value of a network V is given by the formula shown here.

Related formulas


Vvalue of a network (dimensionless)
aReed’s coefficient (dimensionless)
nnetwork nodes (dimensionless)