Non-fungible tokens (NFTs) as a decentralized proof of ownership represent one of the main reasons why Ethereum is a disruptive technology. This paper presents the first systematic study of the interactions occurring in a number of NFT ecosystems. We illustrate how to retrieve transaction data available on the blockchain and structure it as a graph-based model. Thanks to this methodology, we are able to study for the first time the topological structure of NFT networks and show that their properties (degree distribution and others) are similar to those of interaction graphs in social networks. Time-dependent analysis metrics, useful to characterize market influencers and interactions between different wallets, are also introduced. Based on those, we identify across a number of NFT networks the widespread presence of both investors accumulating NFTs and individuals who make large profits.