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add method orient to Graph
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‎src/sage/graphs/graph.py‎

Lines changed: 5 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -9596,7 +9596,10 @@ def bipartite_double(self, extended=False):
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from sage.graphs.tutte_polynomial import tutte_polynomial
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from sage.graphs.lovasz_theta import lovasz_theta
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from sage.graphs.partial_cube import is_partial_cube
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from sage.graphs.orientations import strong_orientations_iterator, random_orientation, acyclic_orientations
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from sage.graphs.orientations import orient
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from sage.graphs.orientations import strong_orientations_iterator
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from sage.graphs.orientations import random_orientation
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from sage.graphs.orientations import acyclic_orientations
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from sage.graphs.connectivity import bridges, cleave, spqr_tree
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from sage.graphs.connectivity import is_triconnected
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from sage.graphs.comparability import is_comparability
@@ -9646,6 +9649,7 @@ def bipartite_double(self, extended=False):
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"is_permutation" : "Graph properties",
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"tutte_polynomial" : "Algorithmically hard stuff",
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"lovasz_theta" : "Leftovers",
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"orient" : "Connectivity, orientations, trees",
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"strong_orientations_iterator" : "Connectivity, orientations, trees",
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"random_orientation" : "Connectivity, orientations, trees",
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"acyclic_orientations" : "Connectivity, orientations, trees",

‎src/sage/graphs/orientations.py‎

Lines changed: 169 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -12,6 +12,8 @@
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:widths: 30, 70
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:delim: |
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:meth:`orient` | Return an oriented version of `G` according the input function `f`.
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:meth:`acyclic_orientations` | Return an iterator over all acyclic orientations of an undirected graph `G`.
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:meth:`strong_orientations_iterator` | Return an iterator over all strong orientations of a graph `G`
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:meth:`random_orientation` | Return a random orientation of a graph `G`
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@@ -28,7 +30,7 @@
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# ****************************************************************************
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# Copyright (C) 2017 Kolja Knauer <[email protected]>
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# 2017 Petru Valicov <[email protected]>
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# 2017-2023 David Coudert <[email protected]>
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# 2017-2024 David Coudert <[email protected]>
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#
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# This program is free software: you can redistribute it and/or modify
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# it under the terms of the GNU General Public License as published by
@@ -41,6 +43,172 @@
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from sage.graphs.digraph import DiGraph
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def orient(G, f, weighted=None, data_structure=None, sparse=None,
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immutable=None, hash_labels=None):
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r"""
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Return an oriented version of `G` according the input function `f`.
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INPUT:
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- ``f`` -- a function that inputs an edge and outputs an orientation of this
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edge
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- ``weighted`` -- boolean (default: ``None``); weightedness for the oriented
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digraph. By default (``None``), the graph and its orientation will behave
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the same.
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- ``sparse`` -- boolean (default: ``None``); ``sparse=True`` is an alias for
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``data_structure="sparse"``, and ``sparse=False`` is an alias for
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``data_structure="dense"``. Only used when ``data_structure=None``.
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- ``data_structure`` -- string (default: ``None``); one of ``'sparse'``,
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``'static_sparse'``, or ``'dense'``. See the documentation of
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:class:`DiGraph`.
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- ``immutable`` -- boolean (default: ``None``); whether to create a
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mutable/immutable digraph. Only used when ``data_structure=None``.
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* ``immutable=None`` (default) means that the graph and its orientation
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will behave the same way.
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* ``immutable=True`` is a shortcut for ``data_structure='static_sparse'``
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* ``immutable=False`` means that the created digraph is mutable. When used
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to orient an immutable graph, the data structure used is ``'sparse'``
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unless anything else is specified.
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- ``hash_labels`` -- boolean (default: ``None``); whether to include edge
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labels during hashing of the oriented digraph. This parameter defaults to
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``True`` if the graph is weighted. This parameter is ignored when
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parameter ``immutable`` is not ``True``. Beware that trying to hash
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unhashable labels will raise an error.
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OUTPUT: a :class:`DiGraph` object
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.. NOTE::
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This method behaves similarly to method
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:meth:`~sage.graphs.generic_graph.GenericGraph.copy`. That is, the
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returned digraph uses the same data structure by default, unless the
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user asks to use another data structure, and the attributes of the input
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graph are copied.
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EXAMPLES::
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sage: G = graphs.CycleGraph(4); G
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Cycle graph: Graph on 4 vertices
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sage: D = G.orient(lambda e:e if e[0] < e[1] else (e[1], e[0], e[2])); D
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Orientation of Cycle graph: Digraph on 4 vertices
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sage: sorted(D.edges(labels=False))
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[(0, 1), (0, 3), (1, 2), (2, 3)]
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TESTS:
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We make sure that one can get an immutable orientation by providing the
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``data_structure`` optional argument::
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sage: def foo(e):
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....: return e if e[0] < e[1] else (e[1], e[0], e[2])
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sage: G = graphs.CycleGraph(4)
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sage: D = G.orient(foo, data_structure='static_sparse')
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sage: D.is_immutable()
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True
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sage: D = G.orient(foo, immutable=True)
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sage: D.is_immutable()
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True
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Bad input::
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sage: G.orient(foo, data_structure='sparse', sparse=False)
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Traceback (most recent call last):
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...
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ValueError: you cannot define 'immutable' or 'sparse' when 'data_structure' has a value
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sage: G.orient(foo, data_structure='sparse', immutable=True)
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Traceback (most recent call last):
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...
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ValueError: you cannot define 'immutable' or 'sparse' when 'data_structure' has a value
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sage: G.orient(foo, immutable=True, sparse=False)
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Traceback (most recent call last):
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...
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ValueError: there is no dense immutable backend at the moment
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Which backend? ::
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sage: G.orient(foo, data_structure='sparse')._backend
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<sage.graphs.base.sparse_graph.SparseGraphBackend object at ...>
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sage: G.orient(foo, data_structure='dense')._backend
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<sage.graphs.base.dense_graph.DenseGraphBackend object at ...>
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sage: G.orient(foo, data_structure='static_sparse')._backend
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<sage.graphs.base.static_sparse_backend.StaticSparseBackend object at ...>
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sage: G.orient(foo, immutable=True)._backend
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<sage.graphs.base.static_sparse_backend.StaticSparseBackend object at ...>
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sage: G.orient(foo, immutable=True, sparse=True)._backend
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<sage.graphs.base.static_sparse_backend.StaticSparseBackend object at ...>
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sage: G.orient(foo, immutable=False, sparse=True)._backend
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<sage.graphs.base.sparse_graph.SparseGraphBackend object at ...>
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sage: G.orient(foo, immutable=False, sparse=False)._backend
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<sage.graphs.base.sparse_graph.SparseGraphBackend object at ...>
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"""
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# Which data structure should be used ?
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if data_structure is not None:
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# data_structure is already defined so there is nothing left to do
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# here. Did the user try to define too much ?
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if immutable is not None or sparse is not None:
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raise ValueError("you cannot define 'immutable' or 'sparse' "
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"when 'data_structure' has a value")
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# At this point, data_structure is None.
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elif immutable is True:
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data_structure = 'static_sparse'
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if sparse is False:
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raise ValueError("there is no dense immutable backend at the moment")
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elif immutable is False:
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# If the user requests a mutable digraph and input is immutable, we
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# choose the 'sparse' cgraph backend. Unless the user explicitly
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# asked for something different.
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if G.is_immutable():
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data_structure = 'dense' if sparse is False else 'sparse'
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elif sparse is True:
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data_structure = "sparse"
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elif sparse is False:
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data_structure = "dense"
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if data_structure is None:
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from sage.graphs.base.dense_graph import DenseGraphBackend
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if isinstance(G._backend, DenseGraphBackend):
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data_structure = "dense"
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else:
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data_structure = "sparse"
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if weighted is None:
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weighted = G.weighted()
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edges = (f(e) for e in G.edge_iterator())
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D = DiGraph([G, edges], format='vertices_and_edges',
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data_structure=data_structure,
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loops=G.allows_loops(),
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multiedges=G.allows_multiple_edges(),
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name=f"Orientation of {G.name()}",
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pos=copy(G._pos), weighted=weighted,
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hash_labels=hash_labels)
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attributes_to_copy = ('_assoc', '_embedding')
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for attr in attributes_to_copy:
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if hasattr(G, attr):
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copy_attr = {}
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old_attr = getattr(G, attr)
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if isinstance(old_attr, dict):
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for v, value in old_attr.items():
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try:
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copy_attr[v] = value.copy()
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except AttributeError:
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copy_attr[v] = copy(value)
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setattr(D, attr, copy_attr)
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else:
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setattr(D, attr, copy(old_attr))
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return D
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def acyclic_orientations(G):
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r"""
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Return an iterator over all acyclic orientations of an undirected graph `G`.

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