Andrew Odlyzko and Benjamin Tilly of the University of Minnesota have written a paper arguing that Metcalfe’s Law, a rule of thumb that computes the value of communication networks, is overly optimistic.

“The fundamental fallacy underlying Metcalfe’s (Law) is in the assumption that all connections or all groups are equally valuable,” the researchers report.

The researchers propose a less dramatic rule of thumb: the value of a network with n members is not n squared, but rather n times the logarithm of n. That means, for example, that the total value of two networks with 1,048,576 members each is only 5 percent more valuable together compared to separate. Metcalfe’s Law predicts a 100 percent increase in value by merging the networks.