Parsing full-fledged predicate-argument structures in a deep syntax framework requires graphs to be predicted. Using the DeepBank (Flickinger et al., 2012) and the Predicate-Argument Structure treebank (Miyao and Tsujii, 2005) as a test field, we show how transition-based parsers, extended to handle connected graphs, benefit from the use of topologically different syntactic features such as dependencies, tree fragments, spines or syntactic paths, bringing a much needed context to the parsing models, improving notably over long distance dependencies and elided coordinate structures. By confirming this positive impact on an accurate 2nd-order graph-based parser (Martins and Almeida, 2014), we establish a new state-of-the-art on these data sets.