In some cases, normal market conditions are displaced by periods of active price manipulation. During these occasions, Metcalfe's Law would not apply due to the atypical activity.

Metcalfe's Law applied to periods of price manipulation

Since the constant of proportionality, A, for Metcalfe's network cannot be seen directly, there may be potential inaccuracies in the data because the data cannot be approximated through the value of A exactly. A may also rise over a period of time with n, which could change Metcalfe's value inaccurately by applying  n^2 to each increase.

Observance of Metcalfe's constant of proportionality

In Metcalfe's Law, a single type of value between connections, such as Bitcoin, is assumed. Although this is applicable for cryptocurrencies, the network law might not work in areas such as social networks, which involve many kinds of media that do not always have a  defined value, compared to the singular type of value for Bitcoin and other cryptocurrencies.

Connections in Metcalfe's Law

If there are other kinds of cryptocurrencies and no Bitcoin in a wallet, than the n proportion would be overstated, which would lead to inaccuracies in Metcalfe's Law.

Inclusion of other cryptocurrencies when calculating Metcalfe value

- Metcalfe's Law applied to periods of price manipulation
- Observance of Metcalfe's constant of proportionality
- Connections in Metcalfe's Law
- Inclusion of other cryptocurrencies when calculating Metcalfe value

Grinnell College

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

 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

Potential inaccuracies of Metcalfe's Law

- Usage of lognormal values to approximate Metcalfe values
- Usage of Gompertz curve to correct Metcalfe's Law

Mitigations of inaccuracies in Metcalfe's Law

It has been found that Metcalfe's Law has outperformed other types of network laws when adjusting for value.

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