In this paper we present a graph-based approach aimed at learning a lexical taxonomy automatically starting from a domain corpus and the Web. Unlike many taxonomy learning approaches in the literature, our novel algorithm learns both concepts and relations entirely from scratch via the automated extraction of terms, definitions and hypernyms. This results in a very dense, cyclic and possibly disconnected hypernym graph. The algorithm then induces a taxonomy from the graph. Our experiments show that we obtain high-quality results, both when building brand-new taxonomies and when reconstructing WordNet sub-hierarchies.