transitive_closure(G, reflexive=False)
The transitive closure 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 there is a path from v to w in G.
Handling of paths from v to v has some flexibility within this definition. A reflexive transitive closure creates a self-loop for the path from v to v of length 0. The usual transitive closure creates a self-loop only if a cycle exists (a path from v to v with length > 0). We also allow an option for no self-loops.
A directed/undirected graph/multigraph.
Determines when cycles create self-loops in the Transitive Closure. If True, trivial cycles (length 0) create self-loops. The result is a reflexive transitive closure of G. If False (the default) non-trivial cycles create self-loops. If None, self-loops are not created.
If :None:None:`reflexive` not in :None:None:`{None, True, False}`
The transitive closure of G
Returns transitive closure of a graph
The treatment of trivial (i.e. length 0) cycles is controlled by the :None:None:`reflexive` parameter.
>>> DG = nx.DiGraph([(1, 2), (2, 3)]) >>> TC = nx.transitive_closure(DG, reflexive=False) >>> TC.edges() OutEdgeView([(1, 2), (1, 3), (2, 3)])
>>> DG = nx.DiGraph([(1, 2), (2, 3), (3, 1)]) >>> TC = nx.transitive_closure(DG, reflexive=False) >>> TC.edges() OutEdgeView([(1, 2), (1, 3), (1, 1), (2, 3), (2, 1), (2, 2), (3, 1), (3, 2), (3, 3)])
>>> DG = nx.DiGraph([(1, 2), (2, 3)]) >>> TC = nx.transitive_closure(DG, reflexive=True) >>> TC.edges() OutEdgeView([(1, 2), (1, 1), (1, 3), (2, 3), (2, 2), (3, 3)])
See :>>> DG = nx.DiGraph([(1, 2), (2, 3), (3, 1)]) >>> TC = nx.transitive_closure(DG, reflexive=None) >>> TC.edges() OutEdgeView([(1, 2), (1, 3), (2, 3), (2, 1), (3, 1), (3, 2)])
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networkx.algorithms.dag.transitive_closure_dag
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