Metcalfe's law: Difference between revisions

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Within the context of social networks, many, including Metcalfe himself, have proposed modified models in which the value of the network grows as ''n'' log ''n'' rather than ''n''<sup>2</sup>.<ref>{{cite web |url=http://vcmike.wordpress.com/2006/08/18/metcalfe-social-networks/ |title=Guest Blogger Bob Metcalfe: Metcalfe's Law Recurses Down the Long Tail of Social Networks |date=18 August 2006 |access-date=2010-06-20}}</ref><ref>B. Briscoe, A. Odlyzko, and B. Tilly, Metcalfe’s law is wrong, ''IEEE Spectrum'' '''43''':7 (2006), pp. 34–39.</ref> 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. Tongia and Wilson also examine the related question of the costs to those excluded.<ref>{{cite web |url=http://ijoc.org/ojs/index.php/ijoc/article/view/873/549 |title=The Flip Side of Metcalfe's Law: Multiple and Growing Costs of Network Exclusion | author = Rahul Tongia and Ernest Wilson| date= September 2007 |access-date=2013-01-15}}</ref>
 
== Validation with actualin 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>{{Citation|doi=10.1016/j.infoecopol.2013.07.002|title=Empirical validation of Metcalfe’s law: How Internet usage patterns have changed over time|first1=António|last1=Madureira|first2=Frank|last2=den Hartog|first3=Harry|last3=Bouwman|author-link3=Harry Bouwman| first4=Nico|last4=Baken|journal=Information Economics and Policy|year=2013}}</ref> A few months later, Metcalfe himself provided further proof, as he used Facebook's data over the past 10 years to show a good fit for Metcalfe's law (the model is ''n<sup>2</sup>'' ).<ref>{{Cite journal|title = Metcalfe's law after 40 years of Ethernet|last = Metcalfe|first = Bob|date = 2013|journal = IEEE Computer|volume = 46|issue = 12|pages = 26–31|doi = 10.1109/MC.2013.374}}</ref>
 
In 2015, Zhang, Liu and Xu extendparameterized the Metcalfe's resultsfunction utilizingin data from [[Tencent]], China's largest social network company, and Facebook. Their work showed that Metcalfe's law held for both, despite the differencedifferences in audience between the two sites; (Facebook serving a worldwide audience and Tencent serving only Chinese users). The Metcalfe's functions offor 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|last2 = Liu|first2 = Jing-Jie|last3 = Xu|first3 = Zhi-Wei}}</ref>
 
In 2018a working paper, Peterson appliedlinked Metcalfe'stime-value-of-money lawconcepts to theMetcalfe [[cryptocurrency]]value using [[Bitcoin]], and showedFacebook thatas Metcalfe'snumerical law determined over 70%examples of Bitcoin'sthe value.proof<ref>{{Cite journal|title = Metcalfe's Law as a Model for Bitcoin's Value|last = Peterson|first = Timothy|date = 20182019|journal title=Bitcoin AlternativeSpreads InvestmentLike Analysta ReviewVirus|volume journal=Working 7|issue = 2|pages = 9–18Paper|doi = 10.2139/ssrn.30782483356098}}</ref> Inand ain yet2018 unpublishedapplied work,Metcalfe's Petersonlaw providedto athe mathematical[[cryptocurrency]] [[Bitcoin]], derivationshowing that linkedover traditional70% time-value-of-money conceptsvariance toin MetcalfeBitcoin value, andwas usedexplained Bitcoinby andapplying FacebookMetcalfe's aslaw numericalto examplesincreases ofin theBitcoin proofnetwork size. <ref>{{Cite journal|title = BitcoinMetcalfe's SpreadsLaw Likeas a VirusModel for Bitcoin's Value|last = Peterson|first = Timothy|date = 20192018|journal = WorkingAlternative PaperInvestment Analyst Review|volume = 7|issue = 2|pages = 9–18|doi = 10.2139/ssrn.33560983078248}}</ref>
 
== See also ==