Metcalfe's law
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Metcalfe's law states that the value of a telecommunications network is proportional to the square of the number of users
of the system (n2). Since a user cannot connect to itself, the actual calculation is the number of
diagonals and sides in an n-agon (see also the triangular numbers):
- ::::[\frac]
The law is often illustrated with the example of fax machines: A single fax machine is useless, but the value of every fax machine increases with the total number of fax machines in the network, because the total number of people with whom you may send and receive documents increases.
In March 2005, Andrew Odlyzko and Benjamin Tilly published a preliminary paper which concludes Metcalfe's law significantly overestimates the value of adding connections. The rule of thumb becomes: "the value of a network with n members is not n squared, but rather n times the logarithm of n." Their primary justification for this is the idea that not all potential connections in a network are equally valuable. For example, most people call their families a great deal more often than they call strangers in other countries, and so do not derive the full value n from the phone service. In the July 2006 IEEE Spectrum, Bob Briscoe, Odlyzko and Tilly state more succinctly: "Metcalfe's Law is Wrong".
In contrast, Reed's law asserts that Metcalfe's law understates the value of adding connections. Not only is a member connected to the entire network as a whole, but also to many significant subsets of the whole. These subsets add value independent of either the individual or the network as a whole. Including subsets into the calculation of the value of the network increases the value faster than just including individual nodes.
Applications of Metcalfe's law
Metcalfe's Law can be applied to more than just telecommunications devices. Metcalfe's Law can be applied to almost any computer systems that exchange data. Examples of devices include:
- Telephones
- FAXs
- Operating systems
- Applications
- Social networking Websites
The same law can be applied to other technological systems, such as personal genome sequencing. As more human genomes are sequenced and tied to personal health information in an interconnected system, the value of the information that a personal genome can contribute to personal health grows.
See also
- Network effect
- Reed's law
- McCandlish's Foil to Reed and Metcalfe (humor)
External links
- [Metcalfe's Law is Wrong]. Bob Briscoe, Andrew Odlyzko, and Benjamin Tilly, July 2006 IEEE Spectrum.
- [ZDNet: Metcalfe's Law overshoots the mark]
- [Andrew Odlyzko and Benjamin Tilly paper]
- [Metcalfe's Law in Reverse], applying Metcalfe's law to form an argument in favour of large, unified networks.
- [George Church. The Personal Genome Project. Molecular Systems Biology. 13 December 2005]
- [IEEE Spectrum article] which claims that Metcalfe's Law is wrong, that the value is closer to n log(n)
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