Merge branch 'public/28603' of git://trac.sagemath.org/sage into publ…

…ic/28626

src/sage/geometry/polyhedron/combinatorial_polyhedron/base.pyx

@@ -48,9 +48,9 @@ Obtaining edges and ridges::
     sage: C.ridges(names=False)[:2]
     ((6, 7), (5, 7))
 
-Edge-graph and ridge-graph::
+Vertex-graph and ridge-graph::
 
-    sage: C.edge_graph()
+    sage: C.vertex_graph()
     Graph on 16 vertices
     sage: C.ridge_graph()
     Graph on 8 vertices
@@ -929,6 +929,39 @@ cdef class CombinatorialPolyhedron(SageObject):
         cdef size_t j
         return tuple((vertex_one(j), vertex_two(j)) for j in range(self._n_edges))
 
+    def vertex_graph(self, names=True):
+        r"""
+        Return a graph in which the vertices correspond to vertices
+        of the polyhedron, and edges to bounded rank 1 faces.
+
+        If ``names`` is set to ``False``, the Vrepresentatives will
+        carry names according to the indexing of the Vrepresentation.
+
+        EXAMPLES::
+
+            sage: P = polytopes.cyclic_polytope(3,5)
+            sage: C = CombinatorialPolyhedron(P)
+            sage: C.vertex_graph()
+            Graph on 5 vertices
+            sage: G = C.vertex_graph()
+            sage: sorted(G.degree())
+            [3, 3, 4, 4, 4]
+
+            sage: P = Polyhedron(rays=[[1]])
+            sage: C = CombinatorialPolyhedron(P)
+            sage: C.graph()
+            Graph on 1 vertex
+        """
+        vertices = self.vertices(names=names)
+
+        # Getting the bounded edges.
+        edges = tuple(edge for edge in self.edges(names=names)
+                      if edge[0] in vertices and edge[1] in vertices)
+
+        return Graph([vertices, edges], format="vertices_and_edges")
+
+    graph = vertex_graph
+
     def edge_graph(self, names=True):
         r"""
         Return the edge graph.
@@ -941,11 +974,15 @@ cdef class CombinatorialPolyhedron(SageObject):
             sage: P = polytopes.cyclic_polytope(3,5)
             sage: C = CombinatorialPolyhedron(P)
             sage: C.edge_graph()
+            doctest:...: DeprecationWarning: the method edge_graph of CombinatorialPolyhedron is deprecated; use vertex_graph
+            See https://trac.sagemath.org/28603 for details.
             Graph on 5 vertices
             sage: G = C.edge_graph()
             sage: sorted(G.degree())
             [3, 3, 4, 4, 4]
         """
+        from sage.misc.superseded import deprecation
+        deprecation(28603, "the method edge_graph of CombinatorialPolyhedron is deprecated; use vertex_graph", 3)
         return Graph(self.edges(names=names), format="list_of_edges")
 
     def ridges(self, add_equalities=False, names=True):