## Tokenomics Layer

These graphs represent the historical decentralisation of
*token ownership* for various blockchain systems. Each
metric is calculated based on the distribution of tokens across
the addresses / entities that held them in each time period.
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##### Nakamoto coefficient

The Nakamoto coefficient represents the minimum number of entities that collectively control more than 50% of the resources (in this case, the majority of circulating tokens at a given point in time).

##### Gini coefficient

The Gini coefficient represents the degree of inequality in a distribution. Values close to 0 indicate equality (all entities in the system control the same amount of assets) and values close to 1 indicate inequality (one entity holds most or all tokens).

##### Shannon Entropy

###### Shannon entropy (also known as information entropy) represents the expected amount of information in a distribution . Typically, a higher value of entropy indicates higher decentralization (lower predictability).

##### HHI

The Herfindahl-Hirschman Index (HHI) is a measure of market concentration. It is defined as the sum of the squares of the market shares (as whole numbers, e.g. 40 for 40%) of the entities in the system. Values close to 0 indicate low concentration (many entities hold a similar number of tokens) and values close to 10,000 indicate high concentration (one entity controls most or all tokens).

##### Theil index

The Theil index captures the lack of diversity, or the redundancy, in a population. In practice, it is calculated as the maximum possible entropy minus the observed entropy. Values close to 0 indicate equality and values towards infinity indicate inequality.

##### Max power ratio

The max power ratio represents the share of tokens that are
owned by the most "**powerful**" entity, i.e. the wealthiest
entity.

##### τ-decentralization index

The τ-decentralization index is a generalization of the Nakamoto coefficient. It is defined as the minimum number of entities that collectively control more than a fraction τ of the total resources (in this case more than 66% of the total tokens in circulation).