O(V + E)
Breadth-first search
Explore in rings, and the first path you find is the shortest.
Breadth-first and depth-first search, cycle detection, topological sort and Dijkstra's shortest path, one page each, all on the same small graph - with and without a cycle.
Explore in rings, and the first path you find is the shortest.
Follow one branch to the end, then back up.
Three colours, and a back edge gives it away.
An order where every dependency comes first.
Always expand the cheapest frontier vertex.