If you had the only telephone in the world, who would you call? Networks seem to grow more valuable to a user proportionately with the number of other users he or she can call. In a network with N users, each sees a value proportional to the N-1 others, so the total value of the network grows as N*(N-1), or as N squared for large N.
Robert Metcalfe, Metcalfe’s Law: A network becomes more valuable as it reaches more users, From the Ether, Infoworld, October 2, 1995.
…we propose another rough rule, that the value of a network of size n grows like n log(n). This rule, while not meant to be exact, does appear to be consistent with historical behavior of networks with regard to interconnection, and it captures the advantage that general connectivity offers over broadcast networks that deliver content. It also helps explain the failure of the dot-com and telecom ventures, since it implies network effects are not as strong as had been hoped for.
Andrew Odlyzko & Benjamin Tilly, A refutation of Metcalfe’s Law and a better estimate for the value of networks and network interconnections, March 2, 2005.
