Entity Linking (EL) and Word Sense Disambiguation (WSD) both address the lexical ambiguity of language. But while the two tasks are pretty similar, they differ in a fundamental respect: in EL the textual mention can be linked to a named entity which may or may not contain the exact mention, while in WSD there is a perfect match between the word form (better, its lemma) and a suitable word sense. In this paper we present Babelfy, a unified graph-based approach to EL and WSD based on a loose identification of candidate meanings coupled with a densest subgraph heuristic which selects high-coherence semantic interpretations. Our experiments show state-of-the-art performances on both tasks on 6 different datasets, including a multilingual setting. Babelfy is online at http://babelfy.org