As of September 2019, Monero is the most capitalized privacy-preserving cryptocurrency, and is ranked tenth among all cryptocurrencies. Monero’s on-chain data privacy guarantees, i.e., how mixins are selected in each transaction, have been extensively studied. However, despite Monero’s prominence, the network of peers running Monero clients has not been analyzed. Such analysis is of prime importance, since potential vulnerabilities in the peer-to-peer network may lead to attacks on the blockchain’s safety (e.g., by isolating a set of nodes) and on users’ privacy (e.g., tracing transactions flow in the network). This paper provides the first step study on understanding Monero’s peer-to-peer (P2P) network. In particular, we deconstruct Monero’s P2P protocol based on its source code, and develop a toolset to explore Monero’s network, which allows us to infer its topology, size, node distribution, and node connectivity. During our experiments, we collected 510 GB of raw data, from which we extracted 21,678 IP addresses of Monero nodes distributed in 970 autonomous systems. We show that Monero’s network is highly centralized—13.2% of the nodes collectively maintain 82.86% of the network connections. We have identified approximately 2,758 active nodes per day, which is 68.7% higher than the number reported by the MoneroHash mining pool. We also identified all concurrent outgoing connections maintained by Monero nodes with very high probability (on average 97.98% for nodes with less than 250 outgoing connections, and 93.79% for nodes with more connections).