How do I check if a directed graph is acyclic?

Question

How do I check if a directed graph is acyclic? And how is the algorithm called? I would appreciate a reference.

Answer 1

The solution given by ShuggyCoUk is incomplete because it might not check all nodes.

def isDAG(nodes V):
    while there is an unvisited node v in V:
        bool cycleFound = dfs(v)
        if cyclefound:
            return false
    return true

This has timecomplexity O(n+m) or O(n^2)