This paper describes a framework for the automated estimation of vessel tortuosity in retinal images. We introduce a new tortuosity metric that takes into account vessel thickness, yielding estimates plausibly closer to intuition and medical judgement than those from previous metrics. We also propose an algorithm identifying automatically a vasculature segment connecting two points specified manually. Starting from a binary image of the vasculature, the algorithm computes a skeletal (medial axis) representation on which all terminal and branching points are located. This is then converted to a graph representation including connectivity as well as thickness information for all vessels. Target segments for tortuosity estimation are identified automatically from end points selected manually using a shortest-path algorithm. Results are presented and compared with those provided by clinical classification on 50 vessels from DRIVE images. An overall agreement with clinical judgement of 92.4% is achieved, superior to that of comparison measures.