Metcalfe's law attempts to describe the value of a network (originally intended for use with telecoms). It states that the value of a network is the square of the number of users, or nodes. 
This can be extended to decentralized networks, such as cryptocurrencies, that rely on a strong network effect to grow and exert influence. Bitcoin has the widest adoption and thus the strongest network effect – a powerful moat differentiating it from other cryptos.
I first found out about the relationship between Metcalfe's law and cryptocurrencies in this 2014 bitcointalk post. It's frequently mentioned in similar discussions of BTC valuation. I attempted to revise the law to suit developments in the currency since 2014. I downloaded price history and unique active addresses per day from blockchain.info, smoothed them over 7-day periods, and compared the two. The equation is V = C*N^2, where V is the Metcalfe value, C is a constant, and N is the number of users.
Here's the initial period:
In late 2014, the relationship changes and a new constant is required. The initial constant of 0.43 that traced an agreeable fit for the first four years of Bitcoin’s life is no longer appropriate. From 2015 onwards, a much smaller constant (0.072) is necessary.
This means that each user’s individual contribution to the network was radically reduced in late 2014. An explanation: the hash rate exploded in mid-2014. New, dedicated mining tech and consolidated mining collectives made mining uneconomical for all but the most sophisticated operators.
Is this an illicit transformation? Is it really fair to retrace the relationship based on a new constant? Clearly, the state of affairs materially changed in 2014. The first graph doesn't fit the data from 2014-16.
I'd like to hear from you. Do you think Metcalfe's law actually applies to cryptos? Is it fair to change the constant to suit the data? Does this have any predictive power?
Thanks for reading. This is my first proper post on Steemit, I'm still getting the hang of this website. Let me know in the comments if I should be doing anything differently. I'm relatively new to cryptos so I'm approaching this with an open mind. I look forward to posting more in the future. - Nic
you may find this video on how currency value emerges from network effects useful.
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Would be interesting to see you recalculate now that it appears market cap has caught up with Metcalf's Law.
http://nakamotoinstitute.org/mempool/how-we-know-bitcoin-is-not-a-bubble/
The Metcalf plot in here is also not fitting too well in 2012 and 2013H1. But your graph is still different. Would you be able to update? Curious where we are at nowadays
I'd love for you to re-visit this and re-chart... or does anyone have anything with all of the more recent data up through mid-2017?
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