transitive_closure#
- transitive_closure(G, reflexive=False)[source]#
Returns transitive closure of a graph
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.
- Parameters:
- GNetworkX Graph
A directed/undirected graph/multigraph.
- reflexiveBool or None, optional (default: False)
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.
- Returns:
- NetworkX graph
The transitive closure of
G
- Raises:
- NetworkXError
If
reflexive
not in{None, True, False}
References
Examples
The treatment of trivial (i.e. length 0) cycles is controlled by the
reflexive
parameter.Trivial (i.e. length 0) cycles do not create self-loops when
reflexive=False
(the default):>>> DG = nx.DiGraph([(1, 2), (2, 3)]) >>> TC = nx.transitive_closure(DG, reflexive=False) >>> TC.edges() OutEdgeView([(1, 2), (1, 3), (2, 3)])
However, nontrivial (i.e. length greater then 0) cycles create self-loops when
reflexive=False
(the default):>>> 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)])
Trivial cycles (length 0) create self-loops when
reflexive=True
:>>> 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)])
And the third option is not to create self-loops at all when
reflexive=None
:>>> 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)])