Metcalfe's law is wrong - communications networks increase in value as they add members-but by how much?

Abstract

This paper argues that Metcalfe's law, which states that the value of a communications network is proportional to the square of the number of its users, is incorrect. By seeming to assure that the value of a network would increase quadratically - proportionately to the square of the number of its participants - while costs would, at most, grow linearly, Metcalfe's law gave an air of credibility to the mad rush for growth and the neglect of profitability. The paper discusses the fundamental flaw of Metcalfe's law and describes how Zipf's law can be used as basis to justify the n log(n) rule-of-thumb valuation of a general communications network of size n.