# Reed's Law

## Description

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## Variables

V | value of a network (dimensionless) |

a | Reed’s coefficient (dimensionless) |

n | network nodes (dimensionless) |