Metcalfe's law
Encyclopedia
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, 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.) 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. The law is also very much related to economics and business management, especially with competitive companies looking to merge with one another.
s 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. 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. 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. 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. Reverse network effects promote individualism, allowing people to not just follow the system, but almost create their own.
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.
Telecommunications network
A telecommunications network is a collection of terminals, links and nodes which connect together to enable telecommunication between users of the terminals. Networks may use circuit switching or message switching. Each terminal in the network must have a unique address so messages or connections...
is proportional to the square
Quadratic growth
In mathematics, a function or sequence is said to exhibit quadratic growth when its values are proportional to the square of the function argument or sequence position, in the limit as the argument or sequence position goes to infinity...
of the number of connected users
of the system (n2). First formulated in this form by George Gilder
George Gilder
George F. Gilder is an American writer, techno-utopian intellectual, Republican Party activist, and co-founder of the Discovery Institute...
in 1993, and attributed to Robert Metcalfe
Robert Metcalfe
Robert Melancton Metcalfe is an electrical engineer from the United States who co-invented Ethernet, founded 3Com and formulated Metcalfe's Law., he is a general partner of Polaris Venture Partners...
in regard to Ethernet
Ethernet
Ethernet is a family of computer networking technologies for local area networks commercially introduced in 1980. Standardized in IEEE 802.3, Ethernet has largely replaced competing wired LAN technologies....
, 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.) 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. The law is also very much related to economics and business management, especially with competitive companies looking to merge with one another.
Network effects
Metcalfe's law characterizes many of the network effectNetwork effect
In economics and business, a network effect is the effect that one user of a good or service has on the value of that product to other people. When network effect is present, the value of a product or service is dependent on the number of others using it.The classic example is the telephone...
s of communication technologies and networks such as the Internet
Internet
The Internet is a global system of interconnected computer networks that use the standard Internet protocol suite to serve billions of users worldwide...
, social networking, and the World Wide Web
World Wide Web
The World Wide Web is a system of interlinked hypertext documents accessed via the Internet...
. 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. 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
Triangular number
A triangular number or triangle number numbers the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n...
n(n − 1)/2, which is proportional to n2 asymptotically
Asymptote
In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity. Some sources include the requirement that the curve may not cross the line infinitely often, but this is unusual for modern authors...
. 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. 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
Fax
Fax , sometimes called telecopying, is the telephonic transmission of scanned printed material , normally to a telephone number connected to a printer or other output device...
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. 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. Reverse network effects promote individualism, allowing people to not just follow the system, but almost create their own.
Limitations
Metcalfe's law is more of a heuristicHeuristic
Heuristic refers to experience-based techniques for problem solving, learning, and discovery. Heuristic methods are used to speed up the process of finding a satisfactory solution, where an exhaustive search is impractical...
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.
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.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. 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.See also
- SimplexSimplexIn geometry, a simplex is a generalization of the notion of a triangle or tetrahedron to arbitrary dimension. Specifically, an n-simplex is an n-dimensional polytope which is the convex hull of its n + 1 vertices. For example, a 2-simplex is a triangle, a 3-simplex is a tetrahedron,...
- List of eponymous laws
- The generalized network effectNetwork effectIn economics and business, a network effect is the effect that one user of a good or service has on the value of that product to other people. When network effect is present, the value of a product or service is dependent on the number of others using it.The classic example is the telephone...
of microeconomicsMicroeconomicsMicroeconomics is a branch of economics that studies the behavior of how the individual modern household and firms make decisions to allocate limited resources. Typically, it applies to markets where goods or services are being bought and sold...
. - Reed's lawReed's lawReed's law is the assertion of David P. Reed that the utility of large networks, particularly social networks, can scale exponentially with the size of the network....
- Sarnoff's lawSarnoff's lawSarnoff's law states that the value of a broadcast network is directly proportional to the number of viewers. It is attributed to David Sarnoff.For example, a network with 100 members is 10 times as valuable as a network with 10 members.-See also:...
- Beckstrom's LawBeckstrom's lawIn economics, Beckstrom's law is a model or theorem formulated by Rod Beckstrom. It purports to answer "the decades old question of 'how valuable is a network.'" According to its creator, it can be used to value any network be it social networks, electronic networks, support groups and even the...
- social mediaSocial mediaThe term Social Media refers to the use of web-based and mobile technologies to turn communication into an interactive dialogue. Andreas Kaplan and Michael Haenlein define social media as "a group of Internet-based applications that build on the ideological and technological foundations of Web 2.0,...
External links
- 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 OdlyzkoAndrew OdlyzkoAndrew Michael Odlyzko is a mathematician and a former head of the University of Minnesota's Digital Technology Center.In the field of mathematics he has published extensively on analytic number theory, computational number theory, cryptography, algorithms and computational complexity,...
, 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.