Algorithm for Finding Redundant Edges in a Graph or Tree

Question

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,

Answer 1

Several ways to attack this, but first you're going to need to define the problem a little more precisely. First, the graph you have here is acyclic and directed: will this always be true?

Next, you need to define what you mean by a "redundant edge". In this case, you start with a graph which has two paths a->c: one via b and one direct one. From this I infer that by "redundant" you mean something like this. Let G=< V, E > be a graph, with V the set of vertices and E ⊆ V×V the set of edges. It kinda looks like you're defining all edges from v_i to v_j shorter than the longest edge as "redundant". So the easiest thing would be to use depth first search, enumerate the paths, and when you find a new one that's longer, save it as the best candidate.

I can't imagine what you want it for, though. Can you tell?