Metcalfe’s Law states that the value of a network increases proportionately with the number participating in the network. Mathematically the value is approximately the square of the number of nodes, or more accurately n(n-1). For example if 20 connected people purchased an iphone, the value of the network created through the connected purchases is 380.
Originally developed to calculate the value of communications networks (Metcalfe was the inventor of the Ethernet), it was posteriorly applied to calculate potential network effects in the early internet days and through the dot-com era: ‘…the idea is that a network is more valuable the more people you can call or write to or the more Web pages you can link to.’ (Briscoe et al 2006). But what is value? Can it be quanitified? Is the same level of value achieved irrespective of the qualities of a node? The fundamental error of Metcalfe’s Law (as also recognised by Metcalfe himself) lies in the assumption that all connections are of equal value. Briscoe et al attribute this valuable observation being first made by Henry David Thoreau in 1854 where he wrote of one of the first telecommunication networks “We are in great haste to construct a magnetic telegraph from Maine to Texas; but Maine and Texas, it may be, have nothing important to communicate.”
Briscoe et al explain “In general, connections are not all used with the same intensity. In fact, in large networks, such as the internet, with millions and millions of potential connections between individuals, most are not used at all. So assigning equal value to all of them is not justified.’ Their alternative then? It also has limitations but its calculation is more modest: n log(n). ‘In our view, much of the difference between the artificial values of the dot-com era and the genuine value created by the Internet can be explained by the difference between Metcalfe-fueled optimism of nsquared and the more sober reality of n log(n). It’s an important re-calculation to be aware of for it provides a more sensible estimation of network growth which needs to be accounted for in merger and acquisitions, telecommunication expansions and potential connectivity.
Resources
References
Briscoe, Odlyzko and Tilly (2006). ‘Metcalfe’s Law is Wrong’ in IEEE Spectrum Vol: 43 Issue: 7 ISSN: 0018-9235 Date: 07/2006 Start Page: 35
