move method is_biconnected from graph.py to connectivity.pyx

Author: dcoudert

src/sage/graphs/connectivity.pyx

@@ -22,6 +22,7 @@ Here is what the module can do:
     :meth:`connected_components_sizes` | Return the sizes of the connected components as a list.
     :meth:`blocks_and_cut_vertices` | Return the blocks and cut vertices of the graph.
     :meth:`blocks_and_cuts_tree` | Return the blocks-and-cuts tree of the graph.
+    :meth:`is_biconnected` | Check whether the graph is biconnected.
     :meth:`biconnected_components` | Return the list of biconnected components.
     :meth:`biconnected_components_subgraphs` | Return a list of biconnected components as graph objects.
     :meth:`number_of_biconnected_components` | Return the number of biconnected components.
@@ -92,7 +93,7 @@ def is_connected(G, forbidden_vertices=None):
 
     .. SEEALSO::
 
-        - :meth:`~Graph.is_biconnected`
+        - :meth:`~sage.graphs.generic_graph.GenericGraph.is_biconnected`
 
     EXAMPLES::
 
@@ -507,7 +508,7 @@ def blocks_and_cut_vertices(G, algorithm='Tarjan_Boost', sort=False, key=None):
 
         - :meth:`blocks_and_cuts_tree`
         - :func:`sage.graphs.base.boost_graph.blocks_and_cut_vertices`
-        - :meth:`~Graph.is_biconnected`
+        - :meth:`~sage.graphs.generic_graph.GenericGraph.is_biconnected`
         - :meth:`~Graph.bridges`
 
     EXAMPLES:
@@ -718,7 +719,7 @@ def blocks_and_cuts_tree(G):
     .. SEEALSO::
 
         - :meth:`~sage.graphs.generic_graph.GenericGraph.blocks_and_cut_vertices`
-        - :meth:`~Graph.is_biconnected`
+        - :meth:`~sage.graphs.generic_graph.GenericGraph.is_biconnected`
 
     EXAMPLES::
 
@@ -780,6 +781,46 @@ def blocks_and_cuts_tree(G):
     return g
 
 
+def is_biconnected(G):
+    r"""
+    Check whether the graph is biconnected.
+
+    A biconnected graph is a connected graph on two or more vertices that is not
+    broken into disconnected pieces by deleting any single vertex.
+
+    .. SEEALSO::
+
+        - :meth:`~sage.graphs.generic_graph.GenericGraph.is_connected`
+        - :meth:`~sage.graphs.generic_graph.GenericGraph.blocks_and_cut_vertices`
+        - :meth:`~sage.graphs.generic_graph.GenericGraph.blocks_and_cuts_tree`
+        - :wikipedia:`Biconnected_graph`
+
+    EXAMPLES::
+
+        sage: G = graphs.PetersenGraph()
+        sage: G.is_biconnected()
+        True
+        sage: G.add_path([0,'a','b'])
+        sage: G.is_biconnected()
+        False
+        sage: G.add_edge('b', 1)
+        sage: G.is_biconnected()
+        True
+
+    TESTS::
+
+        sage: Graph().is_biconnected()
+        False
+        sage: Graph(1).is_biconnected()
+        False
+        sage: graphs.CompleteGraph(2).is_biconnected()
+        True
+    """
+    if G.order() < 2 or not G.is_connected():
+        return False
+    return not G.blocks_and_cut_vertices()[1]
+
+
 def biconnected_components(G):
     r"""
     Return the list of biconnected components.
@@ -867,7 +908,7 @@ def number_of_biconnected_components(G):
     .. SEEALSO::
 
         - :meth:`~sage.graphs.generic_graph.GenericGraph.blocks_and_cut_vertices`
-        - :meth:`~Graph.is_biconnected`
+        - :meth:`~sage.graphs.generic_graph.GenericGraph.is_biconnected`
 
     EXAMPLES:
 
@@ -3466,7 +3507,7 @@ cdef class TriconnectivitySPQR:
     .. SEEALSO::
 
         - :meth:`sage.graphs.connectivity.spqr_tree`
-        - :meth:`~Graph.is_biconnected`
+        - :meth:`~sage.graphs.generic_graph.GenericGraph.is_biconnected`
         - :wikipedia:`SPQR_tree`
 
     EXAMPLES:
@@ -4892,7 +4933,7 @@ def is_triconnected(G):
     .. SEEALSO::
 
         - :meth:`~sage.graphs.generic_graph.GenericGraph.is_connected`
-        - :meth:`~Graph.is_biconnected`
+        - :meth:`~sage.graphs.generic_graph.GenericGraph.is_biconnected`
         - :meth:`~sage.graphs.connectivity.spqr_tree`
         - :wikipedia:`SPQR_tree`
 

src/sage/graphs/generic_graph.py

@@ -236,14 +236,15 @@
     :widths: 30, 70
     :delim: |
 
-    :meth:`~GenericGraph.is_connected` | Test whether the (di)graph is connected.
+    :meth:`~GenericGraph.is_connected` | Check whether the (di)graph is connected.
     :meth:`~GenericGraph.connected_components` | Return the list of connected components
     :meth:`~GenericGraph.connected_components_number` | Return the number of connected components.
     :meth:`~GenericGraph.connected_components_subgraphs` | Return a list of connected components as graph objects.
     :meth:`~GenericGraph.connected_component_containing_vertex` | Return a list of the vertices connected to vertex.
     :meth:`~GenericGraph.connected_components_sizes` | Return the sizes of the connected components as a list.
     :meth:`~GenericGraph.blocks_and_cut_vertices` | Compute the blocks and cut vertices of the graph.
     :meth:`~GenericGraph.blocks_and_cuts_tree` | Compute the blocks-and-cuts tree of the graph.
+    :meth:`~GenericGraph.is_biconnected` | Check whether the graph is biconnected.
     :meth:`~GenericGraph.biconnected_components` | Return the list of biconnected components.
     :meth:`~GenericGraph.biconnected_components_subgraphs` | Return a list of biconnected components as graph objects.
     :meth:`~GenericGraph.number_of_biconnected_components` | Return the number of biconnected components.
@@ -26003,6 +26004,7 @@ def is_self_complementary(self):
         connected_components_sizes,
         connected_components_subgraphs,
         edge_connectivity,
+        is_biconnected,
         is_connected,
         is_cut_edge,
         is_cut_vertex,

src/sage/graphs/graph.py

@@ -1754,46 +1754,6 @@ def is_cactus(self):
         B = self.blocks_and_cut_vertices()[0]
         return len(self.faces()) == sum(1 for b in B if len(b) > 2) + 1
 
-    @doc_index("Graph properties")
-    def is_biconnected(self):
-        """
-        Test if the graph is biconnected.
-
-        A biconnected graph is a connected graph on two or more vertices that is
-        not broken into disconnected pieces by deleting any single vertex.
-
-        .. SEEALSO::
-
-            - :meth:`~sage.graphs.generic_graph.GenericGraph.is_connected`
-            - :meth:`~sage.graphs.generic_graph.GenericGraph.blocks_and_cut_vertices`
-            - :meth:`~sage.graphs.generic_graph.GenericGraph.blocks_and_cuts_tree`
-            - :wikipedia:`Biconnected_graph`
-
-        EXAMPLES::
-
-            sage: G = graphs.PetersenGraph()
-            sage: G.is_biconnected()
-            True
-            sage: G.add_path([0,'a','b'])
-            sage: G.is_biconnected()
-            False
-            sage: G.add_edge('b', 1)
-            sage: G.is_biconnected()
-            True
-
-        TESTS::
-
-            sage: Graph().is_biconnected()
-            False
-            sage: Graph(1).is_biconnected()
-            False
-            sage: graphs.CompleteGraph(2).is_biconnected()
-            True
-        """
-        if self.order() < 2 or not self.is_connected():
-            return False
-        return not self.blocks_and_cut_vertices()[1]
-
     @doc_index("Graph properties")
     def is_block_graph(self):
         r"""

src/sage/graphs/isgci.py

@@ -144,7 +144,7 @@
 
    * - Biconnected
 
-     - :meth:`~sage.graphs.graph.Graph.is_biconnected`,
+     - :meth:`~sage.graphs.generic_graph.GenericGraph.is_biconnected`,
        :meth:`~sage.graphs.generic_graph.GenericGraph.blocks_and_cut_vertices`,
        :meth:`~sage.graphs.generic_graph.GenericGraph.blocks_and_cuts_tree`
 

src/sage/graphs/matching_covered_graph.py

@@ -2387,8 +2387,8 @@ def is_biconnected(self):
         .. NOTE::
 
             This method overwrites the
-            :meth:`~sage.graphs.graph.Graph.is_biconnected` method
-            in order to return ``True`` as matching covered graphs are
+            :meth:`~sage.graphs.generic_graph.GenericGraph.is_biconnected`
+            method in order to return ``True`` as matching covered graphs are
             biconnected.
 
         EXAMPLES: