gh-37260: extend `all_paths_iterator` and `all_simple_paths` to Graph
    
This answer a question from
https://ask.sagemath.org/question/75715/all_simple_paths-generates-
attributeerror-for-graphs/

We make methods `all_paths_iterator` and `all_simple_paths` work for
both `Graph` and `DiGraph`.

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URL: #37260
Reported by: David Coudert
Reviewer(s): John H. Palmieri

Author: Release Manager

src/sage/graphs/digraph.py

@@ -57,8 +57,6 @@
     :widths: 30, 70
     :delim: |
 
-    :meth:`~DiGraph.all_paths_iterator` | Return an iterator over the paths of ``self``.
-    :meth:`~DiGraph.all_simple_paths` | Return a list of all the simple paths of ``self`` starting with one of the given vertices.
     :meth:`~DiGraph.all_cycles_iterator` | Return an iterator over all the cycles of ``self`` starting with one of the given vertices.
     :meth:`~DiGraph.all_simple_cycles` | Return a list of all simple cycles of ``self``.
 
@@ -4379,6 +4377,3 @@ def _singleton_in_branching():
     from sage.graphs.connectivity import strongly_connected_components_subgraphs
     from sage.graphs.connectivity import strongly_connected_component_containing_vertex
     from sage.graphs.connectivity import strong_articulation_points
-    from sage.graphs.path_enumeration import _all_paths_iterator
-    from sage.graphs.path_enumeration import all_paths_iterator
-    from sage.graphs.path_enumeration import all_simple_paths

src/sage/graphs/generic_graph.py

@@ -122,6 +122,8 @@
     :meth:`~GenericGraph.minimum_cycle_basis` | Return a minimum weight cycle basis of the graph.
     :meth:`~GenericGraph.cycle_basis` | Return a list of cycles which form a basis of the cycle space of ``self``.
     :meth:`~GenericGraph.all_paths` | Return a list of all paths (also lists) between a pair of vertices in the (di)graph.
+    :meth:`~GenericGraph.all_paths_iterator` | Return an iterator over the paths of ``self``.
+    :meth:`~GenericGraph.all_simple_paths` | Return a list of all the simple paths of ``self`` starting with one of the given vertices.
     :meth:`~GenericGraph.triangles_count` | Return the number of triangles in the (di)graph.
     :meth:`~GenericGraph.shortest_simple_paths` | Return an iterator over the simple paths between a pair of vertices.
 
@@ -24863,6 +24865,9 @@ def is_self_complementary(self):
     rooted_product = LazyImport('sage.graphs.graph_decompositions.graph_products', 'rooted_product')
     from sage.graphs.path_enumeration import shortest_simple_paths
     from sage.graphs.path_enumeration import all_paths
+    from sage.graphs.path_enumeration import _all_paths_iterator
+    from sage.graphs.path_enumeration import all_paths_iterator
+    from sage.graphs.path_enumeration import all_simple_paths
     from sage.graphs.traversals import lex_BFS
     from sage.graphs.traversals import lex_UP
     from sage.graphs.traversals import lex_DFS

src/sage/graphs/path_enumeration.pyx

@@ -1439,6 +1439,21 @@ def _all_paths_iterator(self, vertex, ending_vertices=None,
 
     EXAMPLES::
 
+        sage: G = graphs.CompleteGraph(4)
+        sage: list(G._all_paths_iterator(1, ending_vertices=[3], simple=True))
+        [[1, 3], [1, 0, 3], [1, 2, 3], [1, 0, 2, 3], [1, 2, 0, 3]]
+        sage: list(G.shortest_simple_paths(1, 3))
+        [[1, 3], [1, 0, 3], [1, 2, 3], [1, 2, 0, 3], [1, 0, 2, 3]]
+        sage: pi = G._all_paths_iterator(1, ending_vertices=[3])
+        sage: for _ in range(6):
+        ....:     print(next(pi))
+        [1, 3]
+        [1, 0, 3]
+        [1, 2, 3]
+        [1, 0, 1, 3]
+        [1, 0, 2, 3]
+        [1, 2, 0, 3]
+
         sage: g = DiGraph({'a': ['a', 'b'], 'b': ['c'], 'c': ['d'], 'd': ['c']}, loops=True)
         sage: pi = g._all_paths_iterator('a', ending_vertices=['d'], report_edges=True, simple=True)
         sage: list(pi)
@@ -1536,6 +1551,11 @@ def _all_paths_iterator(self, vertex, ending_vertices=None,
     if max_length < 1:
         return
 
+    if self.is_directed():
+        neighbor_iterator = self.neighbor_out_iterator
+    else:
+        neighbor_iterator = self.neighbor_iterator
+
     cdef dict my_dict = {}
     cdef dict edge_multiplicity
     if not data:
@@ -1579,7 +1599,7 @@ def _all_paths_iterator(self, vertex, ending_vertices=None,
                 # for further extension, but just yield it immediately. See
                 # trac #12385.
                 frozen_path = frozenset(path)
-                for neighbor in self.neighbor_out_iterator(path[-1]):
+                for neighbor in neighbor_iterator(path[-1]):
                     if neighbor not in frozen_path:
                         queue.append(path + [neighbor])
                     elif (neighbor == path[0] and
@@ -1600,7 +1620,7 @@ def _all_paths_iterator(self, vertex, ending_vertices=None,
                             yield newpath
             else:
                 # Non-simple paths requested: we add all of them
-                for neighbor in self.neighbor_out_iterator(path[-1]):
+                for neighbor in neighbor_iterator(path[-1]):
                     queue.append(path + [neighbor])
 
         if not queue:
@@ -1686,6 +1706,21 @@ def all_paths_iterator(self, starting_vertices=None, ending_vertices=None,
 
     EXAMPLES::
 
+        sage: G = graphs.CompleteGraph(4)
+        sage: list(G.all_paths_iterator(starting_vertices=[1], ending_vertices=[3], simple=True))
+        [[1, 3], [1, 0, 3], [1, 2, 3], [1, 0, 2, 3], [1, 2, 0, 3]]
+        sage: list(G.shortest_simple_paths(1, 3))
+        [[1, 3], [1, 0, 3], [1, 2, 3], [1, 2, 0, 3], [1, 0, 2, 3]]
+        sage: pi = G.all_paths_iterator(starting_vertices=[1], ending_vertices=[3])
+        sage: for _ in range(6):
+        ....:     print(next(pi))
+        [1, 3]
+        [1, 0, 3]
+        [1, 2, 3]
+        [1, 0, 1, 3]
+        [1, 0, 2, 3]
+        [1, 2, 0, 3]
+
         sage: g = DiGraph({'a': ['a', 'b'], 'b': ['c'], 'c': ['d'], 'd': ['c']}, loops=True)
         sage: pi = g.all_paths_iterator(starting_vertices=['a'], ending_vertices=['d'], report_edges=True, simple=True)
         sage: list(pi)
@@ -1909,6 +1944,33 @@ def all_simple_paths(self, starting_vertices=None, ending_vertices=None,
 
     EXAMPLES::
 
+        sage: G = graphs.CompleteGraph(4)
+        sage: G.all_simple_paths([1], [3])
+        [[1, 3], [1, 0, 3], [1, 2, 3], [1, 0, 2, 3], [1, 2, 0, 3]]
+        sage: list(G.shortest_simple_paths(1, 3))
+        [[1, 3], [1, 0, 3], [1, 2, 3], [1, 2, 0, 3], [1, 0, 2, 3]]
+        sage: G.all_simple_paths([0, 1], [2, 3])
+        [[1, 2],
+         [1, 3],
+         [0, 2],
+         [0, 3],
+         [0, 1, 2],
+         [0, 1, 3],
+         [0, 2, 3],
+         [0, 3, 2],
+         [1, 0, 2],
+         [1, 0, 3],
+         [1, 2, 3],
+         [1, 3, 2],
+         [1, 0, 2, 3],
+         [1, 0, 3, 2],
+         [1, 2, 0, 3],
+         [1, 3, 0, 2],
+         [0, 1, 2, 3],
+         [0, 1, 3, 2],
+         [0, 2, 1, 3],
+         [0, 3, 1, 2]]
+
         sage: g = DiGraph({0: [0, 1], 1: [2], 2: [3], 3: [2]}, loops=True)
         sage: g.all_simple_paths()
         [[3, 2],