trac #27408: Merged with 8.9.beta3

src/doc/en/reference/graphs/index.rst

@@ -14,7 +14,7 @@ Graph objects and methods
    sage/graphs/graph
    sage/graphs/digraph
    sage/graphs/bipartite_graph
-
+   sage/graphs/views
 
 Constructors and databases
 --------------------------

src/module_list.py

@@ -446,6 +446,9 @@ def uname_specific(name, value, alternative):
     Extension('sage.graphs.base.boost_graph',
               sources = ['sage/graphs/base/boost_graph.pyx']),
 
+    Extension('sage.graphs.views',
+              sources = ['sage/graphs/views.pyx']),
+
     ################################
     ##
     ## sage.groups

src/sage/combinat/cluster_algebra_quiver/quiver.py

@@ -43,6 +43,7 @@
 from copy import copy
 from sage.rings.all import ZZ, CC, infinity
 from sage.graphs.all import Graph, DiGraph
+from sage.graphs.views import EdgesView
 from sage.combinat.cluster_algebra_quiver.quiver_mutation_type import QuiverMutationType, QuiverMutationType_Irreducible, QuiverMutationType_Reducible, _edge_list_to_matrix
 from sage.combinat.cluster_algebra_quiver.mutation_class import _principal_part, _digraph_mutate, _matrix_to_digraph, _dg_canonical_form, _mutation_class_iter, _digraph_to_dig6, _dig6_to_matrix
 from sage.combinat.cluster_algebra_quiver.mutation_type import _connected_mutation_type, _mutation_type_from_data, is_mutation_finite
@@ -453,7 +454,7 @@ def __init__(self, data, frozen=None, user_labels=None):
 
         # if data is a list of edges, the appropriate digraph is constructed.
 
-        elif isinstance(data, list) and all(isinstance(x, (list,tuple)) for x in data):
+        elif isinstance(data, (list, EdgesView)) and all(isinstance(x, (list,tuple)) for x in data):
             dg = DiGraph(data)
             self.__init__(data=dg, frozen=frozen)
 

src/sage/combinat/root_system/type_C.py

@@ -221,7 +221,7 @@ def dynkin_diagram(self):
             O---O=<=O
             1   2   3
             C3
-            sage: e = c.edges(); e.sort(); e
+            sage: c.edges(sort=True)
             [(1, 2, 1), (2, 1, 1), (2, 3, 1), (3, 2, 2)]
 
              sage: b = CartanType(['C',1]).dynkin_diagram()

src/sage/graphs/comparability.pyx

@@ -707,7 +707,7 @@ def is_permutation(g, algorithm="greedy", certificate=False, check=True,
             return False, co_certif
 
         # Building the two orderings
-        tmp = co_certif.edges(labels=False, sort=False)
+        tmp = list(co_certif.edges(labels=False, sort=False))
         for u,v in certif.edge_iterator(labels=False):
             co_certif.add_edge(v,u)
         certif.add_edges(tmp)

src/sage/graphs/connectivity.pyx

@@ -2261,15 +2261,15 @@ def spqr_tree(G, algorithm="Hopcroft_Tarjan", solver=None, verbose=0):
         sage: T = G.spqr_tree(algorithm="cleave")
         sage: Counter(u[0] for u in T)
         Counter({'R': 1})
-        sage: for u,v in G.edges(labels=False, sort=False):
+        sage: for u,v in list(G.edges(labels=False, sort=False)):
         ....:     G.add_path([u, G.add_vertex(), G.add_vertex(), v])
         sage: T = G.spqr_tree(algorithm="Hopcroft_Tarjan")
         sage: sorted(Counter(u[0] for u in T).items())
         [('P', 15), ('R', 1), ('S', 15)]
         sage: T = G.spqr_tree(algorithm="cleave")
         sage: sorted(Counter(u[0] for u in T).items())
         [('P', 15), ('R', 1), ('S', 15)]
-        sage: for u,v in G.edges(labels=False, sort=False):
+        sage: for u,v in list(G.edges(labels=False, sort=False)):
         ....:     G.add_path([u, G.add_vertex(), G.add_vertex(), v])
         sage: T = G.spqr_tree(algorithm="Hopcroft_Tarjan")
         sage: sorted(Counter(u[0] for u in T).items())

src/sage/graphs/digraph.py

@@ -168,6 +168,7 @@
 from sage.graphs.dot2tex_utils import have_dot2tex
 from sage.misc.misc_c import prod
 from sage.categories.cartesian_product import cartesian_product
+from sage.graphs.views import EdgesView
 
 class DiGraph(GenericGraph):
     r"""
@@ -668,9 +669,10 @@ def __init__(self, data=None, pos=None, loops=None, format=None,
         if (format is None            and
             isinstance(data, list)    and
             len(data) == 2            and
-            isinstance(data[0], list) and # a list of two lists, the second of
-            isinstance(data[1], list) and # which contains iterables (the edges)
-            (not data[1] or callable(getattr(data[1][0], "__iter__", None)))):
+            isinstance(data[0], list) and    # a list of two lists, the second of
+            ((isinstance(data[1], list) and  # which contains iterables (the edges)
+              (not data[1] or callable(getattr(data[1][0], "__iter__", None)))) or
+             (isinstance(data[1], EdgesView)))):
             format = "vertices_and_edges"
 
         if format is None and isinstance(data, dict):
@@ -706,8 +708,8 @@ def __init__(self, data=None, pos=None, loops=None, format=None,
             format = 'int'
             data = 0
 
-        # Input is a list of edges
-        if format is None and isinstance(data,list):
+        # Input is a list of edges or an EdgesView
+        if format is None and isinstance(data, (list, EdgesView)):
             format = "list_of_edges"
             if weighted is None:
                     weighted = False

src/sage/graphs/generic_graph.py

@@ -71,7 +71,7 @@
     :meth:`~GenericGraph.delete_multiedge` | Delete all edges from ``u`` to ``v``.
     :meth:`~GenericGraph.set_edge_label` | Set the edge label of a given edge.
     :meth:`~GenericGraph.has_edge` | Check whether ``(u, v)`` is an edge of the (di)graph.
-    :meth:`~GenericGraph.edges` | Return a list of edges.
+    :meth:`~GenericGraph.edges` | Return a :class:`~EdgesView` of edges.
     :meth:`~GenericGraph.edge_boundary` | Return a list of edges ``(u,v,l)`` with ``u`` in ``vertices1``
     :meth:`~GenericGraph.edge_iterator` | Return an iterator over edges.
     :meth:`~GenericGraph.edges_incident` | Return incident edges to some vertices.
@@ -425,6 +425,7 @@
 
 from copy import copy
 
+from sage.graphs.views import EdgesView
 from .generic_graph_pyx import GenericGraph_pyx, spring_layout_fast
 from .dot2tex_utils import assert_have_dot2tex
 
@@ -4356,7 +4357,7 @@ def weight_function(e):
                 v = next(self.vertex_iterator())
             else:
                 v = starting_vertex
-            sorted_edges = self.edges(key=wfunction_float)
+            sorted_edges = sorted(self.edges(sort=False), key=wfunction_float)
             tree = set([v])
             edges = []
             for _ in range(self.order() - 1):
@@ -11483,7 +11484,7 @@ def has_edge(self, u, v=None, label=None):
 
     def edges(self, labels=True, sort=True, key=None):
         r"""
-        Return a list of edges.
+        Return a :class:`~EdgesView` of edges.
 
         Each edge is a triple ``(u, v, l)`` where ``u`` and ``v`` are vertices
         and ``l`` is a label. If the parameter ``labels`` is ``False`` then a
@@ -11503,7 +11504,7 @@ def edges(self, labels=True, sort=True, key=None):
           one argument and returns a value that can be used for comparisons in
           the sorting algorithm
 
-        OUTPUT: A list of tuples. It is safe to change the returned list.
+        OUTPUT: A :class:`~EdgesView`.
 
         .. WARNING::
 
@@ -11562,21 +11563,27 @@ def edges(self, labels=True, sort=True, key=None):
             sage: P.edges(sort=False, key=lambda x: x)
             Traceback (most recent call last):
             ...
-            ValueError: sort keyword is False, yet a key function is given
+            ValueError: sort keyword is not True, yet a key function is given
 
             sage: G = Graph()
             sage: G.add_edge(0, 1, [7])
             sage: G.add_edge(0, 2, [7])
             sage: G.edge_label(0, 1)[0] += 1
             sage: G.edges()
             [(0, 1, [8]), (0, 2, [7])]
+
+        Deprecation warning for ``sort=None`` (:trac:`27408`)::
+
+            sage: G = graphs.HouseGraph()
+            sage: G.edges(sort=None)
+            doctest:...: DeprecationWarning: parameter 'sort' will be set to False by default in the future
+            See https://trac.sagemath.org/27408 for details.
+            [(0, 1, None), (0, 2, None), (1, 3, None), (2, 3, None), (2, 4, None), (3, 4, None)]
         """
-        if (not sort) and key:
-            raise ValueError('sort keyword is False, yet a key function is given')
-        L = list(self.edge_iterator(labels=labels))
-        if sort:
-            L.sort(key=key)
-        return L
+        if sort is None:
+            deprecation(27408, "parameter 'sort' will be set to False by default in the future")
+            sort = True
+        return EdgesView(self, labels=labels, sort=sort, key=key)
 
     def edge_boundary(self, vertices1, vertices2=None, labels=True, sort=False):
         r"""
@@ -16714,9 +16721,9 @@ def weight_function(e):
             else:
                 # Needed to remove labels.
                 if self.is_directed():
-                    G = networkx.DiGraph(self.edges(labels=False, sort=False))
+                    G = networkx.DiGraph(list(self.edges(labels=False, sort=False)))
                 else:
-                    G = networkx.Graph(self.edges(labels=False, sort=False))
+                    G = networkx.Graph(list(self.edges(labels=False, sort=False)))
             G.add_nodes_from(self)
             return networkx.single_source_dijkstra_path(G, u)
 
@@ -16937,9 +16944,9 @@ def weight_function(e):
             else:
                 # Needed to remove labels.
                 if self.is_directed():
-                    G = networkx.DiGraph(self.edges(labels=False, sort=False))
+                    G = networkx.DiGraph(list(self.edges(labels=False, sort=False)))
                 else:
-                    G = networkx.Graph(self.edges(labels=False, sort=False))
+                    G = networkx.Graph(list(self.edges(labels=False, sort=False)))
             G.add_nodes_from(self)
             return networkx.single_source_dijkstra_path_length(G, u)
 
@@ -17840,7 +17847,6 @@ def depth_first_search(self, start, ignore_direction=False,
             [0, 2, 1]
 
         """
-        from sage.misc.superseded import deprecation
         if distance is not None:
             deprecation(19227, "Parameter 'distance' is broken. Do not use.")
 

src/sage/graphs/graph.py

@@ -410,6 +410,7 @@
 from __future__ import print_function, absolute_import
 import six
 from six.moves import range
+import itertools
 
 from copy import copy
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
@@ -421,6 +422,7 @@
 from sage.graphs.digraph import DiGraph
 from sage.graphs.independent_sets import IndependentSets
 from sage.misc.rest_index_of_methods import doc_index, gen_thematic_rest_table_index
+from sage.graphs.views import EdgesView
 
 
 class Graph(GenericGraph):
@@ -1073,17 +1075,18 @@ def __init__(self, data=None, pos=None, loops=None, format=None,
         if (format is None            and
             isinstance(data, list)    and
             len(data) == 2            and
-            isinstance(data[0], list) and # a list of two lists, the second of
-            isinstance(data[1], list) and # which contains iterables (the edges)
-            (not data[1] or callable(getattr(data[1][0], "__iter__", None)))):
+            isinstance(data[0], list) and    # a list of two lists, the second of
+            ((isinstance(data[1], list) and  # which contains iterables (the edges)
+              (not data[1] or callable(getattr(data[1][0], "__iter__", None)))) or
+             (isinstance(data[1], EdgesView)))):
             format = "vertices_and_edges"
 
         if format is None and isinstance(data, dict):
             if not data:
                 format = 'dict_of_dicts'
             else:
                 val = next(iter(data.values()))
-                if isinstance(val, list):
+                if isinstance(val, (list, EdgesView)):
                     format = 'dict_of_lists'
                 elif isinstance(val, dict):
                     format = 'dict_of_dicts'
@@ -1111,8 +1114,8 @@ def __init__(self, data=None, pos=None, loops=None, format=None,
             format = 'int'
             data = 0
 
-        # Input is a list of edges
-        if format is None and isinstance(data, list):
+        # Input is a list of edges or an EdgesView
+        if format is None and isinstance(data, (list, EdgesView)):
             format = "list_of_edges"
             if weighted is None:
                 weighted = False
@@ -1214,9 +1217,8 @@ def __init__(self, data=None, pos=None, loops=None, format=None,
             if weighted is None: weighted = False
             self.allow_loops(loops, check=False)
             self.allow_multiple_edges(True if multiedges else False, check=False)
-            from itertools import combinations
             self.add_vertices(verts)
-            self.add_edges(e for e in combinations(verts,2) if f(*e))
+            self.add_edges(e for e in itertools.combinations(verts,2) if f(*e))
             if loops:
                 self.add_edges((v,v) for v in verts if f(v,v))
 
@@ -2846,8 +2848,8 @@ def treewidth(self, k=None, certificate=False, algorithm=None):
                     return all(cc.treewidth(k) for cc in g.connected_components_subgraphs())
             else:
                 T = [cc.treewidth(certificate=True) for cc in g.connected_components_subgraphs()]
-                tree = Graph([sum([list(t) for t in T], []),
-                              sum([t.edges(labels=False, sort=False) for t in T], [])],
+                tree = Graph([list(itertools.chain(*T)),
+                              list(itertools.chain(*[t.edges(labels=False, sort=False) for t in T]))],
                              format='vertices_and_edges', name="Tree decomposition")
                 v = next(T[0].vertex_iterator())
                 for t in T[1:]:
@@ -3883,11 +3885,10 @@ def orientations(self, data_structure=None, sparse=None):
             yield D
             return
 
-        from itertools import product
         E = [[(u,v,label), (v,u,label)] if u != v else [(u,v,label)]
              for u,v,label in self.edge_iterator()]
         verts = self.vertices()
-        for edges in product(*E):
+        for edges in itertools.product(*E):
             D = DiGraph(data=[verts, edges],
                         format='vertices_and_edges',
                         name=name,
@@ -5544,10 +5545,9 @@ def seidel_switching(self, s, inplace=True):
             sage: G == H
             True
         """
-        from itertools import product
         G = self if inplace else copy(self)
         boundary = self.edge_boundary(s)
-        G.add_edges(product(s, set(self).difference(s)))
+        G.add_edges(itertools.product(s, set(self).difference(s)))
         G.delete_edges(boundary)
         if not inplace:
             return G
@@ -7869,7 +7869,8 @@ def kirchhoff_symanzik_polynomial(self, name='t'):
         from sage.rings.integer_ring import ZZ
         from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 
-        edges = self.edges()
+        # The order of the vertices in each tuple matters, so use a list
+        edges = list(self.edges(sort=False))
         cycles = self.cycle_basis(output='edge')
 
         edge2int = {e: j for j, e in enumerate(edges)}
@@ -8028,7 +8029,7 @@ def ihara_zeta_function_inverse(self):
         from sage.matrix.constructor import matrix
 
         H = self.subgraph(vertices=self.cores(k=2)[1])
-        E = H.edges()
+        E = list(H.edges(sort=False))
         m = len(E)
         # compute (Hashimoto) edge matrix T
         T = matrix(ZZ, 2 * m, 2 * m, 0)

src/sage/graphs/graph_decompositions/graph_products.pyx

@@ -300,7 +300,7 @@ def is_cartesian_product(g, certificate=False, relabeling=False):
     # Edges uv and u'v' such that d(u,u')+d(v,v') != d(u,v')+d(v,u') are also
     # equivalent
 
-    cdef list edges = g_int.edges(labels=False, sort=False)
+    cdef list edges = list(g_int.edges(labels=False, sort=False))
     cdef dict d = g_int.distance_all_pairs()
     cdef int uu, vv
     for i, (u, v) in enumerate(edges):

src/sage/graphs/orientations.py

@@ -196,7 +196,7 @@ def _strong_orientations_of_a_mixed_graph(Dg, V, E):
         sage: from sage.graphs.orientations import _strong_orientations_of_a_mixed_graph
         sage: g = graphs.CycleGraph(5)
         sage: Dg = DiGraph(g) # all edges of g will be doubly oriented
-        sage: it = _strong_orientations_of_a_mixed_graph(Dg, g.vertices(), g.edges(labels=False))
+        sage: it = _strong_orientations_of_a_mixed_graph(Dg, list(g), list(g.edges(labels=False, sort=False)))
         sage: len(list(it)) # there are two orientations of this multigraph
         2
     """

src/sage/graphs/spanning_tree.pyx

@@ -697,7 +697,7 @@ cpdef boruvka(G, wfunction=None, bint check=False, bint by_weight=True):
     If the input graph is a tree, then return its edges::
 
         sage: T = graphs.RandomTree(randint(1, 10))
-        sage: T.edges() == sorted(boruvka(T, check=True))
+        sage: list(T.edges(sort=True)) == sorted(boruvka(T, check=True))
         True
 
     Check if the weight of MST returned by Prim's and Boruvka's is the same::

src/sage/graphs/tutte_polynomial.py

@@ -448,10 +448,9 @@ def __call__(self, graph):
             (0, 1, None)
         """
         degrees = dict(graph.degree_iterator(labels=True))
-        edges = graph.edges(labels=True)
-        edges.sort(key=lambda x: degrees[x[0]]+degrees[x[1]])  # Sort by degree
-        for e in edges:
-            return e
+        edges = graph.edges(labels=True, sort=False)
+        if edges:
+            return min(edges, key=lambda x: degrees[x[0]] + degrees[x[1]])
         raise RuntimeError("no edges left to select")
 
 
@@ -463,15 +462,15 @@ def __call__(self, graph):
             sage: from sage.graphs.tutte_polynomial import MaximizeDegree
             sage: G = graphs.PathGraph(6)
             sage: MaximizeDegree()(G)
-            (3, 4, None)
+            (1, 2, None)
         """
         degrees = dict(graph.degree_iterator(labels=True))
-        edges = graph.edges(labels=True)
-        edges.sort(key=lambda x: degrees[x[0]]+degrees[x[1]])  # Sort by degree
-        for e in reversed(edges):
-            return e
+        edges = graph.edges(labels=True, sort=False)
+        if edges:
+            return max(edges, key=lambda x: degrees[x[0]] + degrees[x[1]])
         raise RuntimeError("no edges left to select")
 
+
 ###########
 # Caching #
 ###########