Metcalfe's law states that the value of a communication system grows as approximately the square of the number of users of the system (N²). Since a user cannot connect to itself, the actual calculation is
- N(N−1), or N²−N.
First formulated by Robert Metcalfe in regard to Ethernet, Metcalfe's law explains many of the network effects of communication technologies and networks such as the Internet and World Wide Web.
The law is often illustrated with the example of fax machines: A single fax machine is useless, but the value of every fax machine increases with the total number of fax machines in the network, because the total number of people with whom you may send and receive documents increases. This contrasts with traditional models of supply and demand, where increasing the quantity of something decreases its value.
In March 2005, Andrew Odlyzko and Benjamin Tilly published a preliminary paper which concludes Metcalfe's Law significantly overestimates the value of adding connections. The rule of thumb becomes: "the value of a network with n members is not n squared, but rather n times the logarithm of n."
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