In the field of computer science, a pre-topological order or pre-topological ordering of a directed graph is a linear ordering of its vertices such that if there is a directed path from vertex "u" to vertex "v" and "v" comes before "u" in the ordering, then there is also a directed path from vertex "v" to vertex "u".
If the graph is a directed acyclic graph (DAG), topological orderings are pre-topological orderings and vice versa. In other cases, any pre-topological ordering gives a partial order.
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