Your algorithm doesn't really work for graphs - it actually treats the vertices as a set of points (the edges are not taken into account, you're just looking fo

Your algorithm doesn't really work for graphs - it actually treats the vertices as a set of points (the edges are not taken into account, you're just looking for the largest Euclidean distance between two points). Unforunately, it is not correct even then. Here is a counterexample: A | B-C-D You have points laid out like this, and: AC > CD=BC, AD=AB < BD. If you start from point C, you will pick A as the lowest point, then B/D, giving you the pair AB/AD as the result. The correct result is BD. Was fun to think about, though!