Given an adjacency matrix or other data based on the nodes, there are many algorithms for determining whether the graph is acyclic (e.g. row reduction or leaf trimming).
If I have only a set of edges (e.g. ${(a,b), (b,c), (d,b)}$), I could obviously convert that into an adjacency matrix and proceed from there.
I'm wondering if there is a good algorithm that works directly with the edges.