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Uniswap is a Constant Product Market Maker built around liquidity pools,where pairs of tokens are exchanged subject to a fee that is proportional tothe size of transactions. At the time of writing, there exist more than 6,000pools associated with Uniswap v3, implying that empirical investigations on thefull ecosystem can easily become computationally expensive. Thus, we propose asystematic workflow to extract and analyse a meaningful but computationallytractable sub-universe of liquidity pools. Leveraging on the 34 pools foundrelevant for the six-months time window January-June 2022, we then investigatethe related liquidity consumption behaviour of market participants. We proposeto represent each liquidity taker by a suitably constructed transaction graph,which is a fully connected network where nodes are the liquidity taker'sexecuted transactions, and edges contain weights encoding the time elapsedbetween any two transactions. We extend the NLP-inspired graph2vec algorithm tothe weighted undirected setting, and employ it to obtain an embedding of theset of graphs. This embedding allows us to extract seven clusters of liquiditytakers, with equivalent behavioural patters and interpretable tradingpreferences. We conclude our work by testing for relationships between thecharacteristic mechanisms of each pool, i.e. liquidity provision, consumption,and price variation. We introduce a related ideal crypto law, inspired from theideal gas law of thermodynamics, and demonstrate that pools adhering to thislaw are healthier trading venues in terms of sensitivity of liquidity andagents' activity. Regulators and practitioners could benefit from our model bydeveloping related pool health monitoring tools.

DeFi: data-driven characterisation of Uniswap v3 ecosystem & an ideal crypto law for liquidity pools