We give a brief explanation of homology and persistent homology intuitively by using matrix representations of boundary operators and introduce a result of the law of large numbers for persistence diagrams of a stationary ergodic point process.We recall the notion of Bitcoin graphs and chainlets and show an example of how to compute persistence diagrams for chainlet matrices by viewing them as point clouds.
The Blockchain technology and, in particular blockchain-based cryptocurrencies, offer us information that has never been seen before in the financial world. In contrast to fiat currencies, all transactions of crypto-currencies and crypto-tokens are permanently recorded on distributed ledgers and are publicly available. This allows us to construct a transaction graph and to assess not only its organization but to glean relationships between transaction graph properties and crypto price dynamics. The goal of this paper is to facilitate our understanding on horizons and limitations of what can be learned on crypto-tokens from local topology and geometry of the Ethereum transaction network whose even global network properties remain scarcely explored. By introducing novel tools based on Topological Data Analysis and Functional Data Depth into Blockchain Data Analytics, we show that Ethereum network (one of the most popular blockchains for creating new crypto-tokens) can provide critical insights on price changes of crypto-tokens that are otherwise largely inaccessible with conventional data sources and traditional analytic methods.