Metcalfe's Law Revisited

TL;DR

This paper revisits Metcalfe's law through mathematical analysis, confirming its validity as a measure of network utility and exploring its limitations and upper bounds in different network models.

Contribution

It establishes a mathematical framework for network value, compares traditional and broader models, and clarifies conditions under which Metcalfe's law holds or reaches its upper limit.

Findings

Metcalfe's law is confirmed as a valid measure of network utility.

Traditional network models do not exhibit Metcalfe's law.

Broader network models validate and define an upper boundary for Metcalfe's law.

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.