Metcalfe's Law Revisited

Abstract

Rudimentary mathematical analysis of simple network models suggests bandwidth-independent saturation of network growth dynamics and hints at linear decrease in information density of the data. However it strongly confirms Metcalfe's law as a measure of network utility and suggests it can play an important role in network calculations. This paper establishes mathematical notion of network value and analyses two conflicting models of network. One, traditional model, fails to manifest Metcalfe's law. Another model, one that observes network in a wider context, both confirms Metcalfe's law and reveals its upper boundary.