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How crypto flows among Bitcoin users is an important question for understanding the structure and dynamics of the cryptoasset at a global scale. We compiled all the blockchain data of Bitcoin from its genesis to the year 2020, identified users from anonymous addresses of wallets, and constructed monthly snapshots of networks by focusing on regular users as big players. We apply the methods of bow-tie structure and Hodge decomposition in order to locate the users in the upstream, downstream, and core of the entire crypto flow. Additionally, we reveal principal components hidden in the flow by using non-negative matrix factorization, which we interpret as a probabilistic model. We show that the model is equivalent to a probabilistic latent semantic analysis in natural language processing, enabling us to estimate the number of such hidden components. Moreover, we find that the bow-tie structure and the principal components are quite stable among those big players. This study can be a solid basis on which one can further investigate the temporal change of crypto flow, entry and exit of big players, and so forth.
XRP is a modern crypto-asset (crypto-currency) developed by Ripple Labs, which has been increasing its financial presence. We study its transaction history available as ledger data. An analysis of its basic statistics, correlations, and network prope
In this study, we investigate the flow of money among bank accounts possessed by firms in a region by employing an exhaustive list of all the bank transfers in a regional bank in Japan, to clarify how the network of money flow is related to the econo
The arisen of Bitcoin has led to much enthusiasm for blockchain research and block mining, and the extensive existence of mining pools helps its participants (i.e., miners) gain reward more frequently. Recently, the mining pools are proved to be vuln
Bitcoins Lightning Network (LN) is a scalability solution for Bitcoin allowing transactions to be issued with negligible fees and settled instantly at scale. In order to use LN, funds need to be locked in payment channels on the Bitcoin blockchain (L
Over the last two decades, we have seen a dramatic improvement in the efficiency of conflict-driven clause-learning Boolean satisfiability (CDCL SAT) solvers on industrial problems from a variety of domains. The availability of such powerful general-