rolfsky

The law is usually quoted in terms of growth of the network, but we can run Metcalfe's Law in Reverse and use it to characterize the effect of cutting a network into pieces:

The value of partitioning a network into N isolated components is 1/N'th the value of the original network.

This new law follows directly from the original Metcalfe's Law. Each of the new components has a size of 1/N'th the size of the original network. Thus, its value is 1/(N2) of the original value. At the same time, there are N of these new mini-networks, so the over-all value is N * 1/(N2) = 1/N