Note

This documents the development version of NetworkX. Documentation for the current release can be found here.

networkx.algorithms.dag.transitive_reduction

transitive_reduction(G)[source]

Returns transitive reduction of a directed graph

The transitive reduction of G = (V,E) is a graph G- = (V,E-) such that for all v,w in V there is an edge (v,w) in E- if and only if (v,w) is in E and there is no path from v to w in G with length greater than 1.

Parameters
GNetworkX DiGraph

A directed acyclic graph (DAG)

Returns
NetworkX DiGraph

The transitive reduction of G

Raises
NetworkXError

If G is not a directed acyclic graph (DAG) transitive reduction is not uniquely defined and a NetworkXError exception is raised.

References

https://en.wikipedia.org/wiki/Transitive_reduction

Examples

To perform transitive reduction on a DiGraph:

>>> DG = nx.DiGraph([(1, 2), (2, 3), (1, 3)])
>>> TR = nx.transitive_reduction(DG)
>>> list(TR.edges)
[(1, 2), (2, 3)]

To avoid unnecessary data copies, this implementation does not return a DiGraph with node/edge data. To perform transitive reduction on a DiGraph and transfer node/edge data:

>>> DG = nx.DiGraph()
>>> DG.add_edges_from([(1, 2), (2, 3), (1, 3)], color='red')
>>> TR = nx.transitive_reduction(DG)
>>> TR.add_nodes_from(DG.nodes(data=True))
>>> TR.add_edges_from((u, v, DG.edges[u, v]) for u, v in TR.edges)
>>> list(TR.edges(data=True))
[(1, 2, {'color': 'red'}), (2, 3, {'color': 'red'})]