In a network, Metcalfe's value represents the network capacity or the amount of paired connections that can occur. The Metcalfe value would also serve as an upper bound of proportionality.

Value of Metcalfe's Law

The law was intended to find the factor n where total network costs (cn) are recovered. In some cases, a proportionality factor(A) is applied to the model. It would be represented in a more detailed way as cn= M= A * n(n-1)/2.  Using mathematical reasoning through pair-wise connections, the model assumes equality between the users' network connections.

Original design of Metcalfe's Law

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).

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

Network economics of 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 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.

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