Open-source, Decentralized Online Social Networks (DOSNs) are emerging as alternatives to the popular yet centralized and profit-driven platforms like Facebook or Twitter. In DOSNs, users can set up their own server, or instance, while they can actually interact with users of other instances. Moreover, by adopting the same communication protocol, DOSNs become part of a massive social network, namely the Fediverse. Mastodon is the most relevant platform in the Fediverse to date, and also the one that has attracted attention from the research community. Existing studies are however limited to an analysis of a relatively outdated sample of Mastodon focusing on few aspects at a user level, while several open questions have not been answered yet, especially at the instance level. In this work, we aim at pushing forward our understanding of the Fediverse by leveraging the primary role of Mastodon therein. Our first contribution is the building of an up-to-date and highly representative dataset of Mastodon. Upon this new data, we have defined a network model over Mastodon instances and exploited it to investigate three major aspects: the structural features of the Mastodon network of instances from a macroscopic as well as a mesoscopic perspective, to unveil the distinguishing traits of the underlying federative mechanism; the backbone of the network, to discover the essential interrelations between the instances; and the growth of Mastodon, to understand how the shape of the instance network has evolved during the last few years, also when broading the scope to account for instances belonging to other platforms. Our extensive analysis of the above aspects has provided a number of findings that reveal distinguishing features of Mastodon and that can be used as a starting point for the discovery of all the DOSN Fediverse.