sagemathgh-38725: fix issue in edge_cut

    
Fixes sagemath#38713.

We ensure that all algorithms return edges with label when
`algorithm="LP"`.

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### ⌛ Dependencies

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URL: sagemath#38725
Reported by: David Coudert
Reviewer(s): Kwankyu Lee

src/sage/graphs/generic_graph.py

@@ -7512,7 +7512,7 @@ def edge_cut(self, s, t, value_only=True, use_edge_labels=False, vertices=False,
            sage: g.edge_cut(1, 2, value_only=True, algorithm='LP')                      # needs sage.numerical.mip
            3
 
-        :issue:`12797`::
+        Check that :issue:`12797` and :issue:`38713` are fixed::
 
             sage: G = Graph([(0, 3, 1), (0, 4, 1), (1, 2, 1), (2, 3, 1), (2, 4, 1)])
             sage: G.edge_cut(0, 1, value_only=False, use_edge_labels=True)
@@ -7521,7 +7521,7 @@ def edge_cut(self, s, t, value_only=True, use_edge_labels=False, vertices=False,
             sage: G.edge_cut(0, 1, value_only=False, use_edge_labels=True)
             [1, [(2, 1, 1)]]
             sage: G.edge_cut(0, 1, value_only=False, use_edge_labels=True, algorithm='LP')          # needs sage.numerical.mip
-            (1, [(2, 1)])
+            (1, [(2, 1, 1)])
         """
         self._scream_if_not_simple(allow_loops=True)
         if vertices:
@@ -7574,9 +7574,10 @@ def weight(x):
         # frozensets otherwise
         if g.is_directed():
             def good_edge(e):
-                return e
+                return (e[0], e[1])
         else:
-            good_edge = frozenset
+            def good_edge(e):
+                return frozenset((e[0], e[1]))
 
         # Some vertices belong to part 1, others to part 0
         p.add_constraint(v[s], min=0, max=0)
@@ -7589,15 +7590,15 @@ def good_edge(e):
 
             # Adjacent vertices can belong to different parts only if the
             # edge that connects them is part of the cut
-            for x, y in g.edge_iterator(labels=None):
+            for x, y in g.edge_iterator(labels=False):
                 p.add_constraint(v[x] + b[good_edge((x, y))] - v[y], min=0)
 
         else:
             # we minimize the number of edges
             p.set_objective(p.sum(weight(w) * b[good_edge((x, y))] for x, y, w in g.edge_iterator()))
             # Adjacent vertices can belong to different parts only if the
             # edge that connects them is part of the cut
-            for x, y in g.edge_iterator(labels=None):
+            for x, y in g.edge_iterator(labels=False):
                 p.add_constraint(v[x] + b[good_edge((x, y))] - v[y], min=0)
                 p.add_constraint(v[y] + b[good_edge((x, y))] - v[x], min=0)
 
@@ -7612,7 +7613,7 @@ def good_edge(e):
             return obj
 
         answer = [obj]
-        answer.append([e for e in g.edge_iterator(labels=False) if b[good_edge(e)]])
+        answer.append([e for e in g.edge_iterator(labels=True) if b[good_edge(e)]])
 
         if vertices:
             v = p.get_values(v, convert=bool, tolerance=integrality_tolerance)