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networkx.algorithms.dag.topological_sort

topological_sort(G)[source]

Return a generator of nodes in topologically sorted order.

A topological sort is a nonunique permutation of the nodes such that an edge from u to v implies that u appears before v in the topological sort order.

Parameters:

G (NetworkX digraph) – A directed acyclic graph (DAG)
Returns:

An iterable of node names in topological sorted order.
Return type:

iterable
Raises:
  • NetworkXError – Topological sort is defined for directed graphs only. If the graph G is undirected, a NetworkXError is raised.
  • NetworkXUnfeasible – If G is not a directed acyclic graph (DAG) no topological sort exists and a NetworkXUnfeasible exception is raised. This can also be raised if G is changed while the returned iterator is being processed.
  • RuntimeError – If G is changed while the returned iterator is being processed.

Examples

To get the reverse order of the topological sort:

>>> DG = nx.DiGraph([(1, 2), (2, 3)])
>>> list(reversed(list(nx.topological_sort(DG))))
[3, 2, 1]

Notes

This algorithm is based on a description and proof in “Introduction to Algorithms: A Creative Approach” [1] .

See also

is_directed_acyclic_graph(), lexicographical_topological_sort()

References

[1]Manber, U. (1989). Introduction to Algorithms - A Creative Approach. Addison-Wesley.