The global structure of P2P networks underlying modern cryptocurrencies is hidden by design: each node only knows its neighbors and maintains a local \textit{peer table} of IP addresses. The peer table of a node can be seen as the node's ``local view'' of the set of nodes currently in the network: it is constantly updated with information collected from the neighbors and it is used by the node to establish new connections when needed. The maintenance rules of the nodes' peer tables determine the global structure of the network and its evolution. Even though the global structure is unknown to any node of the network as well as to any external observer, the rules for the exchange of information between neighbors are compatible with the design and use of network \textit{crawlers} that can query the nodes and extract some information about their peer tables. In this paper we first analyze the data we crawled from nodes of the Bitcoin and Dogecoin P2P networks, to collect information about the distribution of IP addresses in the peer tables and to estimate the evolution of network size and churn rate; we then use the estimates to set up the parameters for a simulation of the Bitcoin network and we analyze the evolution of the network structure that we get from the simulation. Overall, our results show that Bitcoin's peer-table maintenance rules induce non-uniform, heavy-tailed visibility patterns while nevertheless generating a well-connected and structurally robust network.

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