The project aims to develop new Network Science and Graph Deep Learning models and methods for the advanced analysis of blockchain-based online social media platforms. Web3 is in fact centered on blockchain technology, which allows the integration of cryptocurrencies and tokens into social media platforms, called Blockchain Online Social Media (BOSM) platforms. BOSMs offer their users the opportunity to be rewarded for actions of social influence and to define and transfer digital assets such as non-fungible tokens (NFTs), thus creating a new form of decentralized finance. In this context, the project addresses some research challenges including understanding how social and economic aspects intertwine and influence each other, how wealth is distributed among users, and what factors influence the NFT market.