I have been trying to learn Tarjan's algorithm from Wikipedia for 3 hours now, but I just can't make head or tail of it. :(

http://en.wikipedia.org/wiki/Tarjan's_strongly_connected_components_algorithm#cite_note-1

Why is it a subtree of the DFS tree? (actually DFS produces a forest? o_O) And why does v.lowlink=v.index imply that v is a root?

Can someone please explain this to me / give the intuition or motivation behind this algorithm?

graph depth-first-search tarjans-algorithm
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