Is Topological Sort Stable

An interesting property of a stable topological sort is that cyclic dependencies are tolerated and resolved according to original order of elements in sequence. This is a desirable feature for many applications because it allows to sort any sequence with any imaginable dependencies between the elements.

Why topological sort is not unique?

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 DAG. If a Hamiltonian path exists, the topological sort order is unique; no other order respects the edges of the path.

When can you not use topological sort?

Topological Sorting for a graph is not possible if the graph is not a DAG. For example, a topological sorting of the following graph is “5 4 2 3 1 0”. There can be more than one topological sorting for a graph. For example, another topological sorting of the following graph is “4 5 2 3 1 0”.