Initialize an empty stack for storage of nodes, S.
For each vertex u, define u.visited to be false.
Push the root (first node to be visited) onto S.
While S is not empty:
    Pop the first element in S, u.
    If u.visited = false, then:
        U.visited = true
        for each unvisited neighbor w of u:
            Push w into S.
End process when all nodes have been visited.