Many shallow natural language understanding tasks use dependency trees to extract relations between content words. However, strict surface-structure dependency trees tend to follow the linguistic structure of sentences too closely and frequently fail to provide direct relations between content words... To mitigate this problem, the original Stanford Dependencies representation also defines two dependency graph representations which contain additional and augmented relations that explicitly capture otherwise implicit relations between content words. In this paper, we revisit and extend these dependency graph representations in light of the recent Universal Dependencies (UD) initiative and provide a detailed account of an enhanced and an enhanced++ English UD representation. We further present a converter from constituency to basic, i.e., strict surface structure, UD trees, and a converter from basic UD trees to enhanced and enhanced++ English UD graphs. We release both converters as part of Stanford CoreNLP and the Stanford Parser. (read more)