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Is there an established algorithm for finding redundant edges in a graph?
For example, I’d like to find that a->d and a->e are redundant, and then get rid of them, like this:
=> 
Edit: Strilanc was nice enough to read my mind for me. ‘Redundant’ was too strong of a word, since in the example above, neither a->b or a->c is considered redundant, but a->d is.
You want to compute the smallest graph which maintains vertex reachability.
This is called the transitive reduction of a graph. The wikipedia article should get you started down the right road.