Editing Metcalfe's law (section)

== Validation in data ==
For more than 30 years, there was little concrete evidence in support of the law. Finally, in July 2013, Dutch researchers analyzed European Internet-usage patterns over a long-enough time{{Specify|date=March 2023}} and found <math>n^2</math> proportionality for small values of <math>n</math> and <math>n \log n</math> proportionality for large values of <math>n</math>.<ref>{{cite journal |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 |date=2013 |volume=25 |issue=4 |pages=246–256}}</ref> A few months later, Metcalfe himself provided further proof by using [[Facebook]]'s data over the past 10 years to show a good fit for Metcalfe's law.<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 |s2cid=206448593}}</ref>

In 2015, Zhang, Liu, and Xu parameterized the Metcalfe function in data from [[Tencent]] and Facebook. Their work showed that Metcalfe's law held for both, despite differences in audience between the two sites (Facebook serving a worldwide audience and Tencent serving only Chinese users). The functions for the two sites were <math>V_\text{Tencent}=7.39\times10^{-9}\times n^2 </math> and <math>V_\text{Facebook}=5.70\times 10^{-9}\times n^{2}</math> respectively.<ref>{{Cite journal |title=Tencent and Facebook Data Validate Metcalfe's Law |last1=Zhang |first1=Xing-Zhou |last2=Liu |first2=Jing-Jie |last3=Xu |first3=Zhi-Wei |date=2015 |journal=Journal of Computer Science and Technology |volume=30 |issue=2 |pages=246–251 |doi=10.1007/s11390-015-1518-1 |s2cid=255158958}}</ref>
One of the earliest mentions of the Metcalfe Law in the context of Bitcoin was by a Reddit post by Santostasi in 2014. He compared the observed generalized Metcalfe behavior for Bitcoin to the Zipf's Law and the theoretical Metcalfe result.<ref>{{cite web |url= https://www.reddit.com/r/Bitcoin/comments/21pujs/bitcoin_compared_with_metcalfes_and_zipfs_law/ |title=Bitcoin compared with Metcalfe's and Zipf's law |date=29 March 2014 |access-date=29 March 2014}}</ref>
The Metcalfe's Law is a critical component of Santostasi's Bitcoin Power Law Theory.<ref>{{cite web |url= https://giovannisantostasi.medium.com/the-bitcoin-power-law-theory-962dfaf99ee9/ |title=The Bitcoin Power Law Theory |date=20 March 2024 |access-date=20 March 2024}}</ref>
In a working paper, Peterson linked time-value-of-money concepts to Metcalfe value using Bitcoin and Facebook as numerical examples of the proof,<ref>{{Cite journal |last=Peterson |first=Timothy |date=2019 |title=Bitcoin Spreads Like a Virus |journal=Working Paper |doi=10.2139/ssrn.3356098 |s2cid=159240517}}</ref> and in 2018 applied Metcalfe's law to [[Bitcoin]], showing that over 70% of variance in Bitcoin value was explained by applying Metcalfe's law to increases in Bitcoin network size.<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 |s2cid=158572041}}</ref>

In a 2024 interview, mathematician [[Terence Tao]] emphasized the importance of universality and networking within the mathematics community, for which he cited the Metcalfe's Law. Tao believes that a larger audience leads to more connections, which ultimately results in positive developments within the community. For this, he cited Metcalfe's law to support this perspective. Tao further stated, "my whole career experience has been sort of the more connections equals just better stuff happening".<ref>{{Cite web |last=Strogatz |first=Steven |date=February 1, 2024 |title=What Makes for 'Good' Mathematics? |url=https://www.quantamagazine.org/what-makes-for-good-mathematics-20240201/ |website=Quanta Magazine}}</ref>