![[Wallet Cluster_info.png]] A wallet cluster is a set of wallets that belong to the same entity or activity. For instance, a person owning several hot, cold, and custodial wallets for their assets forms a cluster. Similarly, a DApp, CeFi, or CEX that owns many interconnected wallets to operate their business also forms a cluster of wallets. Clusters can inform us about the true ownership distribution of assets. The complexity of these clusters informs us about the sophistication of the ownership and usage of tokens within the network of holders. A healthy token should feature various degrees of sophistication within its clusters. However, if a token lacks sophisticated clusters of wallets, it indicates that the network of ownership is underdeveloped. We find these connections by identifying strongly connected wallets through the hypergraph $_wG$. Wallets that transfer one way token $\tau_0$ and back the other way token $\tau_1$ are considered more connected. The strength of the clustering coefficient is based on the similarities of the diversity $\mathcal{D}$ of wallets as well as the type of hyperedge assigned between them. Consider the hypergraph $_wG = (V, E)$ where $V$ is the set of nodes representing wallets and $E$ is the set of hyperedges representing transactions involving multiple wallets and tokens. A wallet $v_i$ transfers $\tau_0$ to wallet $v_j$, and wallet $v_j$ transfers $\tau_1$ back to wallet $v_i$. A hyperedge $e$ is formed between $v_i$ and $v_j$ if $e = \{ (v_i, v_j, \tau_0), (v_j, v_i, \tau_1) \}$. The clustering coefficient $C$ for a wallet cluster is based on the similarity of diversity $\mathcal{D}$ of wallets and the type of hyperedge assigned between them. Let $\mathcal{D}(v)$ represent the diversity of wallet $v$. The clustering coefficient $C$ for a cluster of wallets is defined as: $C = \frac{1}{|V|} \sum_{v \in V} \left( \frac{\sum_{e \in E_v} w(e)}{|\mathcal{D}(v)|} \right)$ Where $E_v$ is the set of hyperedges involving wallet $v$ and $w(e)$ is the weight of the hyperedge $e$ based on the type of tokens transacted. A healthy token network should exhibit a variety of sophisticated clusters. Lack of such clusters indicates an underdeveloped network of ownership.