In this paper, we present ContrastMedium, an algorithm that transforms noisy semantic networks into full-fledged, clean taxonomies. ContrastMedium is able to identify the embedded taxonomy structure from a noisy knowledge graph without explicit human supervision such as, for instance, a set of manually selected input root and leaf concepts. This is achieved by leveraging structural information from a companion reference taxonomy, to which the input knowledge graph is linked (either automatically or manually). When used in conjunction with methods for hypernym acquisition and knowledge base linking, our methodology provides a complete solution for end-to-end taxonomy induction. We conduct experiments using automatically acquired knowledge graphs, as well as a SemEval benchmark, and show that our method is able to achieve high performance on the task of taxonomy induction.