Editing Topological sorting (section)

==Uniqueness==
If a topological sort has the property that all pairs of consecutive vertices in the sorted order are connected by edges, then these edges form a directed [[Hamiltonian path]] in the [[Directed acyclic graph|DAG]]. If a Hamiltonian path exists, the topological sort order is unique; no other order respects the edges of the path. Conversely, if a topological sort does not form a Hamiltonian path, the DAG will have two or more valid topological orderings, for in this case it is always possible to form a second valid ordering by swapping two consecutive vertices that are not connected by an edge to each other. Therefore, it is possible to test in linear time whether a unique ordering exists, and whether a Hamiltonian path exists, despite the [[NP-hard]]ness of the Hamiltonian path problem for more general directed graphs (i.e., cyclic directed graphs).{{r|VM}}