The Uniswap v3 ecosystem is built upon liquidity pools, where pairs of tokens are exchanged subject to a fee. We propose a systematic workflow to extract a meaningful but tractable sub-universe out of the current > 6,000 pools. We filter by imposing minimum levels on individual pool features, e.g. liquidity locked and agents’ activity, but also maximising the interconnection between the chosen pools to support broader dynamics. Then, we investigate liquidity consumption behaviour on the most relevant pools for Jan-June 2022. We propose to describe each liquidity taker by a transaction graph, which is a complete graph where nodes are transactions on pools and edges have weights from the time elapsed between pairs of transactions. Each graph is embedded into a vector by our own variant of the NLP rooted graph2vec algorithm. Thus, we are able to investigate the structural equivalence of liquidity takers behaviour and extract seven clusters with interpretable features. Finally, we introduce an ideal crypto law inspired from the ideal gas law of thermodynamics. Our model tests a relationship between variables that govern the mechanisms of each pool, i.e. liquidity provision, consumption, and price variation. If the law is satisfied, we say the pool has high cryptoness and demonstrate that it constitutes a better venue for the activity of market participants. Our metric could be employed by regulators and practitioners for developing pool health monitoring tools and establishing minimum levels of requirements.
