networkx.algorithms.dag.topological_sort¶

topological_sort(G)[source]¶

Returns a generator of nodes in topologically sorted order.

A topological sort is a nonunique permutation of the nodes of a directed graph such that an edge from u to v implies that u appears before v in the topological sort order. This ordering is valid only if the graph has no directed cycles.

Parameters

GNetworkX digraph: A directed acyclic graph (DAG)

Yields

nodes: Yields the nodes in topological sorted order.

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.

See also

is_directed_acyclic_graph, lexicographical_topological_sort

Notes

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

References

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

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]

If your DiGraph naturally has the edges representing tasks/inputs and nodes representing people/processes that initiate tasks, then topological_sort is not quite what you need. You will have to change the tasks to nodes with dependence reflected by edges. The result is a kind of topological sort of the edges. This can be done with networkx.line_graph() as follows:

>>> list(nx.topological_sort(nx.line_graph(DG)))
[(1, 2), (2, 3)]