This article proposes a method to extract dependency structures from phrase-structure level parsing with Interaction Grammars. Interaction Grammars are a formalism which expresses interactions among words using a polarity system. Syntactical composition is led by the saturation of polarities. Interactions take place between constituents, but as grammars are lexicalized, these interactions can be translated at the level of words. Dependency relations are extracted from the parsing process: every dependency is the consequence of a polarity saturation. The dependency relations we obtain can be seen as a refinement of the usual dependency tree. Generally speaking, this work sheds new light on links between phrase structure and dependency parsing.