The proportionality of Metcalfe's Law is derived from the assertion that from n users, and as more people join the network they increase the value. The value of the network in that case is proportional to that of the square of the users(N²).

Network modeling of Metcalfe's Law

Bitcoin can be represented as a network due to the continuous nature of bitcoin price formation. The bitcoin closing price has varied from 1.40 in December 2011 to 9.56 in December 2017, and this increase has been approximated by the correlated growth in Metcalfe Value during that same interval.

Network growth of Bitcoin over time

- Network modeling of Metcalfe's Law
- Network growth of Bitcoin over time

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Metcalfe's law approximates bitcoin's medium or long-term price, using the model of supply and demand. In the law, a network's importance is a function of a number of transaction pairs, and is represented through the formula n(n-1)/2.

Metcalfe's Law

 Peterson, Timothy, Metcalfe's Law as a Model for Bitcoin's Value (January 22, 2018). Alternative Investment Analyst Review, Q2 2018, Vol. 7, No. 2, 9-18., Available at SSRN: https://ssrn.com/abstract=3078248 or http://dx.doi.org/10.2139/ssrn.3078248 

Metcalfe's Law as a Model for Bitcoin's Value

Network economics of Metcalfe's Law

To examine the accuracy of Metcalfe's Law with bitcoin price, the distribution of daily transactions was measured.  Bitcoin price was observed to follow Metcalfe's Law with a R² of about 80%, which is indicative of a high degree of fit.

Accuracy of Metcalfe's Law

- Detection of cryptocurrency price manipulation through Metcalfe's Law

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