This sorts the nodes in a network such that each arc, say k-th, has Tail(k) Head(k) in the renumbered node indexes. This arises in a variety of combinatorial optimization problems, such as those with precedence constraints. If the nodes cannot be topologically sorted, the network does not represent a partially ordered set. This means, for example, there is an inconsistency in the constraints, such as jobs that cannot be sequenced to satisfy the asserted precedence relations.

a listing of the vertices of a graph in such an order that all the ordering relations are respected

an ordered search of a DAG (a Directed Acyclic Graph ) where you visit/print each vertex only when you have been to all of it's parent vertices