Metcalfe’s law states that the value of a network is proportional to the square of its total number of users. ERC-20 is a smart contract standard for tokens that run on the Ethereum blockchain. In what is the first study of its kind, we take the 50 most valuable of these tokens and apply Metcalfe’s law to value each of the underlying networks and determine whether the relationships between their users and their valuations are indeed quadratic, as the law implies.

Using roughly 14.5 million transactions obtained from the Ethereum blockchain, we create usage metrics based on a count of unique active addresses and run regressions based on Daily, Weekly, and Monthly versions of the metric. Market cap data is used to approximate network value. On an aggregated level we find that using Monthly Active Addresses performs best.

Applying this approach to the 50 individual tokens, we reject our null hypothesis 48 times; Only two tokens have an estimated exponent ​b​ that is not significantly different from 2, as Metcalfe’s law would assert it to be. The actual distribution varies, with the mean being 0.825, suggesting a linear or sub-linear relationship between user growth and network value for these tokens.