### Mathematical Introduction to the Wallet Graph Explicitly, The Wallet Graph is a Hyper-graph$^1$ notated as $_wG$, where $_wG = (W_{\tau},E)$ Where $W$ is the set of wallets holding a token $\tau$ and $E$ is the set of sets of hyperedges, each edge $e_{\tau^n}\;\in\;E = (E_{\tau^1}, E_{\tau^2},\;...\; ,E_{\tau^{N-1}}, E_{\tau^N})$ of $H$ in respect to $\tau$. ie the Hyper-graph for Ethereum is constructed of its transactions as well as the layer 2 transactions on its network. ![[Wallet_graph.png]] We seek to define and meaure the features of $_wG$ as defined below. Our aim is to create a risk score that mathematically considers the general notions of Crypto: Decentralization, Inclusivity, and Fairness. ### Integrating The Wallet Graph into Financial Risk Ratings Xerberus seeks to create metrics rooted in rigours mathematics to provide a **general solution** to on chain risk, to do so, we introduce the mathematics and their generalizations onto our particular use case: mitigation of loss in terms of return and faulty investment. Our Risk Rating stands on two postulates: - The on-chain transactional information contains all relevant information of an asset - there is a general solution for token risk