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'''Metcalfe's law''' states the effect of a [[telecommunications network]] is [[Quadratic growth|proportional to the square]] of the number of connected users
of the system (''n''<sup>2</sup>). First formulated in this form by [[George Gilder]] in 1993,<ref>{{cite book | title = Information Rules | author = Carl Shapiro and Hal R. Varian | publisher = Harvard Business Press | year = 1999 | isbn = 978-0-87584-863-1 | url = https://books.google.com/books?id=aE_J4Iv_PVEC&printsec=frontcover&dq=inauthor:shapiro+inauthor:varian#PPA184,M1 }}</ref> and attributed to [[Robert Metcalfe]] in regard to [[Ethernet]], Metcalfe's law was originally presented, c. 1980, not in terms of users, but rather of "compatible communicating devices" (for example, fax machines, telephones, etc.).<ref>{{cite web | title = Metcalfe's Law: more misunderstood than wrong? | date = July 26, 2006 | author = Simeon Simeonov | work = HighContrast: Innovation & venture capital in the post-broadband era | url = http://simeons.wordpress.com/2006/07/26/metcalfes-law-more-misunderstood-than-wrong/ }}</ref> Only later with the [[history of the Internet|globalization of the Internet]] did this law carry over to users and networks as its original intent was to describe Ethernet purchases and connections.<ref>{{cite web | title = Metcalfe's Law, Web 2.0, and the Semantic Web| date =
==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=https://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
==Limitations==
In addition to the difficulty of quantifying the "value" of a network, the mathematical justification for Metcalfe's law 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''.{{
Metcalfe’s law assumes that the value of each node n is of equal benefit.<ref>{{cite web|author1=Andrew Odlyzko|author2=Bob Briscoe|authorlink1=Andrew Odlyzko|title=Metcalfe's Law is Wrong|url=https://spectrum.ieee.org/computing/networks/metcalfes-law-is-wrong|website=IEEE Spectrum: Technology, Engineering, and Science News|accessdate=25 November 2016|date=1 Jul 2006}}</ref> If this is not the case, for example because the one fax machines serves 50 workers in a company, the second fax machine serves half of that, the third one third, and so on, then the relative value of an additional connection decreases. Likewise, in social networks, if users that join later use the network less than early adopters, then the benefit of each additional user may lessen, making the overall network less efficient if costs per users are fixed.
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== Validation with actual data ==
Despite many arguments about Metcalfe' law, no real data based evidence for or against was available for more than 30 years. Only in July 2013, Dutch researchers managed to analyze European Internet usage patterns over a long enough time and found ''n''<sup>2</sup> proportionality for small values of ''n'' and (''n'' log ''n'') proportionality for large values of ''n''.<ref>{{
In 2015, Zhang, Liu and Xu extend Metcalfe's results utilizing data from [[Tencent]], China's largest social network company, and Facebook. Their work showed that Metcalfe's law held for both, despite the difference in audience between the two sites; Facebook serving a worldwide audience and Tencent serving only Chinese users. The Metcalfe's functions of the two sites given in the paper were <math>V_{Tencent}=7.39\times10^{-9}\times n^{2}</math> and <math>V_{Facebook}=5.70\times 10^{-9}\times n^{2}</math> respectively. <ref>{{Cite journal|title = Tencent and Facebook Data Validate Metcalfe's Law|last = Zhang|first = Xing-Zhou|date = 2015|journal = Journal of Computer Science and Technology|volume = 30|issue = 2|pages = 246–251|doi = 10.1007/s11390-015-1518-1|pmid = |last2 = Liu|first2 = Jing-Jie|last3 = Xu|first3 = Zhi-Wei}}</ref>
In 2018, Peterson applied Metcalfe's law to the [[cryptocurrency]] [[Bitcoin]], and showed that Metcalfe's law determined over 70% of Bitcoin's value.<ref>{{Cite journal|title = Metcalfe's Law as a Model for Bitcoin's Value|last = Peterson|first = Timothy|date = 2018|journal = Alternative Investment Analyst Review|volume = 7|issue = 2|pages = 9–18|doi = 10.2139/ssrn.3078248}}</ref>
== See also ==
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