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Metcalfe's law

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Two telephones can make only one connection, five can make 10 connections, and twelve can make 66 connections.

Metcalfe's law states that the value of a telecommunications network is proportional to the square of the number of connected users of the system (n²). First formulated in this form by George Gilder in 1993,^[1] and attributed to Robert Metcalfe in regard to Ethernet, Metcalfe's law was originally presented, circa 1980, not in terms of users, but rather of "compatible communicating devices" (for example, fax machines, telephones, etc.)^[2] Only more recently with the launch of the internet did this law carry over to users and networks as its original intent was to describe Ethernet purchases and connections.^[3] The law is also very much related to economics and business management, especially with competitive companies looking to merge with one another.

Contents  [hide]  1 Network effects 2 Limitations 3 Business practicalities 4 Modified models 5 See also 6 References 7 External links

[edit] Network effects

Metcalfe's law characterizes many of the network effects of communication technologies and networks such as the Internet, social networking, and the World Wide Web. Former Chairman of the U.S. Federal Communications Commission, Reed Hundt, said that this law gives the most understanding to the workings of the internet.^[4] Metcalfe's Law is related to the fact that the number of unique connections in a network of a number of nodes (n) can be expressed mathematically as the triangular number n(n − 1)/2, which is proportional to n² asymptotically. Websites and blogs such as Twitter, Facebook, and Myspace are the most prominent modern example of Metcalfe's Law. Forty five percent of Americans in 2005 said the internet had played a huge role in a major decision in their life as a result of this social networking.^[5] Some of the major decisions involved buying a home, buying a car, inquiring medical help, and discovering a career. Interconnecting two networks is said to greatly exceed the power of the two separate, individual networks.

The law has often been illustrated using 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 each user may send and receive documents increases. Goods characterize the first component or intrinsic network effect. Services fall under the second component of network effects known as complementary.^[6] A social networking site works the same way as the fax machine described above. The greater number of users with the service, the more valuable the service becomes to the community. Deriving from Metcalfe's Law, every new "friend" accepted or added on these social networking sites makes the user's profile ever more valuable in terms of the law. Positive and negative outcomes take place with all network effects involving a service of this sort. New jobs, relationships, and opportunities arise with more people coming together, however, if not used correctly, services of this type can lead to distant relationships.

With so much emphasis on creating a universal communication and networking unit, little thought has been provided regarding signs of a reverse effect. As new members or consumers buy a good or service, others may leave the group to discover alternatives. With fewer users, the consumer is more of a priority to the company's success. On the other hand, with millions of people using a good or service, companies display less of a personal connection because one person is not vital to the success of the whole unit.^[7] Reverse network effects promote individualism, allowing people to not just follow the system, but almost create their own.

[edit] Limitations

Metcalfe's law is more of a heuristic or metaphor than an iron-clad empirical rule. In addition to the difficulty of quantifying the "value" of a network, the mathematical justification measures only the potential number of contacts, i.e., the technological side of a network. However the social utility of a network depends upon the number of nodes in contact. A good way to describe this is "quality versus quantity." There is a fallacious assumption and argument that all networkers present the same value as the other. This is not the case. For example, if Chinese and non-Chinese users do not understand each other, the utility of a network of users that speak the other language is near zero, and the law has to be calculated for the two compatibly communicating sub-networks separately. A barrier is created underneath the umbrella of users that oftentimes is never broken. Therefore, the mathematical equation of Metcalfe's Law posted above lies somewhere in between a linear and quadratic growth curve.

[edit] Business practicalities

With Metcalfe's Law the way it is described, all companies would theoretically combine with another partner. This would create more users involved in the company both on a consumer and supplier basis. This is not the case however. Much of the time, only companies of equal equity are willing to interconnect with one another. In the case of a larger network or business, and a smaller network or business, the larger feels the smaller one is benefiting on a much larger scale. The larger business gains little in comparison to the small company as the large has already developed a reputation whereas the small company is feeding off their previous success.^[8]

[edit] Modified models

Within the context of social networks, many, including Metcalfe himself, have proposed modified models using logarithmic and linear proportionality rather than squared proportionality.^[9] Reed and Odlyzko have sought out possible relationships to Metcalfe's Law in terms of describing the relationship of a network and one can read about how those are related.^[10]

[edit] See also

• Simplex
• List of eponymous laws
• The generalized network effect of microeconomics.
• Reed's law
• Sarnoff's law
• Beckstrom's Law
• social media

[edit] References

1. ^ Carl Shapiro and Hal R. Varian (1999). Information Rules. Harvard Business Press. ISBN 087584863X. http://books.google.com/books?id=aE_J4Iv_PVEC&printsec=frontcover&dq=inauthor:shapiro+inauthor:varian#PPA184,M1. 
2. ^ Simeon Simeonov (July 26, 2006). "Metcalfe’s Law: more misunderstood than wrong?". HighContrast: Innovation & venture capital in the post-broadband era. http://simeons.wordpress.com/2006/07/26/metcalfes-law-more-misunderstood-than-wrong/. 
3. ^ James Hendler and Jennifer Golbeck (2008). "Metcalfe's Law, Web 2.0, and the Semantic Web". http://www.cs.umd.edu/~golbeck/downloads/Web20-SW-JWS-webVersion.pdf. 
4. ^ Bob Briscoe (July 2006). "Metcalfe's Law is wrong". http://spectrum.ieee.org/computing/networks/metcalfes-law-is-wrong. Retrieved 2010-07-25. 
5. ^ Jeffrey Boase (25 January 2006). "The Strength of Internet Ties". http://www.pewinternet.org/~/media//Files/Reports/2006/PIP_Internet_ties.pdf.pdf. Retrieved 2010-07-25. 
6. ^ R. Tongia. "The Dark Side of Metcalfe’s Law: Multiple and Growing Costs of Network Exclusion". http://www.cstep.in/docs/Network%20Exclusion%209-22-09.pdf. Retrieved 2010-07-25. 
7. ^ Bernard Lunn (16 March 2009). "Researchers: Is There a Reverse Network Effect with Scale?". http://www.readwriteweb.com/archives/is_there_a_reverse_network_effect_with_scale.php. Retrieved 2010-07-25. 
8. ^ Steven Shankland (15 March 2005). "Researchers: Metcalfe's Law overshoots the mark". http://www.zdnet.com/news/researchers-metcalfes-law-overshoots-the-mark/141783. Retrieved 2010-07-25. 
9. ^ "Guest Blogger Bob Metcalfe: Metcalfe’s Law Recurses Down the Long Tail of Social Networks". 18 August 2006. http://vcmike.wordpress.com/2006/08/18/metcalfe-social-networks/. Retrieved 2010-06-20. 
10. ^ Rahul Tongia (September 2007). "TURNING METCALFE ON HIS HEAD: THE MULTIPLE COSTS OF NETWORK EXCLUSION". http://web.si.umich.edu/tprc/papers/2007/772/TPRC-07-Exclusion-Tongia%26Wilson.pdf. Retrieved 2010-07-25. 

[edit] External links

Wikibooks has a book on the topic of The Information Age

• Metcalfe's Law: More Misunderstood Than Wrong?. A co-worker of Bob Metcalfe puts the IEEE Spectrum critique in perspective. Republished here.
• Metcalfe's Law is Wrong. Bob Briscoe, Andrew Odlyzko, and Benjamin Tilly, July 2006 IEEE Spectrum. Points out that Metcalfe's Law is wrong, that the value is closer to n log (n)
• Metcalfe’s Law Recurses Down the Long Tail of Social Networking by Bob Metcalfe
• 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
• The Semantic Web and Metcalfe's Law
• A Group Is Its Own Worst Enemy. Clay Shirky's keynote speech on Social Software at the O'Reilly Emerging Technology conference, Santa Clara, April 24, 2003. The fourth of his "Four Things to Design For" is: "And, finally, you have to find a way to spare the group from scale. Scale alone kills conversations, because conversations require dense two-way conversations. In conversational contexts, Metcalfe's law is a drag."
• How Many Facebook Friends Does Someone Need.
• The Dark Side of Metcalfe's Law.
• Globalization Transformation.

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