Metcalfe's law: Difference between revisions

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→‎Network effects: Updated equation of n(n+1)/2 to be n(n-1)/2. A quick check shows the updated equation results in f(2) = 1, f(3) = 3, f(4) = 6, f(5) = 10, f(6) = 15, etc.
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==Network effects==
Metcalfe's law characterizes many of the [[network effect]]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.<ref>{{cite web |url=http://spectrum.ieee.org/computing/networks/metcalfes-law-is-wrong |title= Metcalfe's Law is wrong | author = Bob Briscoe, Andrew Odlyzko and Benjamin Tilly | date= July 2006 |accessdate=2010-07-25}}</ref> Metcalfe's Law is related to the fact that the number of unique possible connections in a network of <math>n</math> nodes can be expressed mathematically as the [[triangular number]] <math>n(n+-1)/2</math>, which is [[Big O notation|asymptotically]] proportional to <math>n^2</math>.
 
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.<ref>{{cite web |url=http://www.cstep.in/uploads/default/files/publications/stuff/CSTEP_The_Dark_Side_of_Metcalfe%E2%80%99s_Law_Confpaper_2009.pdf |title=The Dark Side of Metcalfe’s Law: Multiple and Growing Costs of Network Exclusion | author = R. Tongia | date= |accessdate=2017-12-19}}</ref> Likewise, in social networks, the greater number of users with the service, the more valuable the service becomes to the community.