This paper describes the design and use of the graph-based parsing framework and toolkit UniParse, released as an open-source python software package. UniParse as a framework novelly streamlines research prototyping, development and evaluation of graph-based dependency parsing architectures. UniParse does this by enabling highly efficient, sufficiently independent, easily readable, and easily extensible implementations for all dependency parser components. We distribute the toolkit with ready-made configurations as re-implementations of all current state-of-the-art first-order graph-based parsers, including even more efficient Cython implementations of both encoders and decoders, as well as the required specialised loss functions.