Algorithm for Finding Redundant Edges in a Graph or Tree

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.