gh-35718: `sage.graphs`: More modularization
    
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### 📚 Description

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Mostly using `lazy_import` and adding `# optional` annotations to
doctests.
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- Part of: #29705
- Cherry-picked from: #35095

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- [ ] I have created tests covering the changes.
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URL: #35718
Reported by: Matthias Köppe
Reviewer(s): David Coudert, Matthias Köppe

Author: Release Manager

src/sage/graphs/all.py

@@ -4,7 +4,7 @@
 lazy_import("sage.graphs.graph_generators", "graphs")
 lazy_import("sage.graphs.digraph_generators", "digraphs")
 lazy_import("sage.graphs.hypergraph_generators", "hypergraphs")
-from .graph_database import GraphDatabase, GenericGraphQuery, GraphQuery
+lazy_import("sage.graphs.graph_database", ["GraphDatabase", "GenericGraphQuery", "GraphQuery"])
 from .graph import Graph
 from .digraph import DiGraph
 from .bipartite_graph import BipartiteGraph
@@ -13,7 +13,7 @@
 import sage.graphs.partial_cube
 from . import graph_list as graphs_list
 lazy_import("sage.graphs", "graph_coloring")
-from .graph_database import graph_db_info
+lazy_import("sage.graphs.graph_database", "graph_db_info")
 lazy_import("sage.graphs.graph_editor", "graph_editor")
 
 from sage.graphs.isgci import graph_classes

src/sage/graphs/base/boost_graph.pyx

@@ -572,7 +572,7 @@ cpdef bandwidth_heuristics(g, algorithm='cuthill_mckee'):
         from sage.graphs.base.boost_graph import bandwidth_heuristics
         sage: bandwidth_heuristics(Graph())
         (0, [])
-        sage: bandwidth_heuristics(graphs.RandomGNM(10,0))
+        sage: bandwidth_heuristics(graphs.RandomGNM(10,0))                              # optional - networkx
         (0, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
 
     """
@@ -1964,8 +1964,8 @@ cpdef diameter_DHV(g, weight_function=None, check_weight=True):
 
     TESTS::
 
-        sage: G = graphs.RandomBarabasiAlbert(17,6)
-        sage: diameter_DHV(G) == G.diameter(algorithm = 'Dijkstra_Boost')
+        sage: G = graphs.RandomBarabasiAlbert(17,6)                                     # optional - networkx
+        sage: diameter_DHV(G) == G.diameter(algorithm = 'Dijkstra_Boost')               # optional - networkx
         True
         sage: G = Graph([(0,1,-1)], weighted=True)
         sage: diameter_DHV(G)

src/sage/graphs/base/c_graph.pyx

@@ -1577,11 +1577,11 @@ cdef class CGraphBackend(GenericGraphBackend):
         We check that the bug described in :trac:`8406` is gone::
 
             sage: G = Graph()
-            sage: R.<a> = GF(3**3)
-            sage: S.<x> = R[]
-            sage: G.add_vertex(a**2)
-            sage: G.add_vertex(x)
-            sage: G.vertices(sort=True)
+            sage: R.<a> = GF(3**3)                                                      # optional - sage.rings.finite_rings
+            sage: S.<x> = R[]                                                           # optional - sage.rings.finite_rings
+            sage: G.add_vertex(a**2)                                                    # optional - sage.rings.finite_rings
+            sage: G.add_vertex(x)                                                       # optional - sage.rings.finite_rings
+            sage: G.vertices(sort=True)                                                 # optional - sage.rings.finite_rings
             [a^2, x]
 
         And that the bug described in :trac:`9610` is gone::
@@ -2107,9 +2107,9 @@ cdef class CGraphBackend(GenericGraphBackend):
 
         Ensure that :trac:`13664` is fixed ::
 
-            sage: W = WeylGroup(["A",1])
-            sage: G = W.cayley_graph()
-            sage: Graph(G).degree()
+            sage: W = WeylGroup(["A",1])                                                # optional - sage.combinat sage.groups
+            sage: G = W.cayley_graph()                                                  # optional - sage.combinat sage.groups
+            sage: Graph(G).degree()                                                     # optional - sage.combinat sage.groups
             [1, 1]
             sage: h = Graph()
             sage: h.add_edge(1,2,"a")
@@ -4406,9 +4406,9 @@ cdef class CGraphBackend(GenericGraphBackend):
 
         TESTS::
 
-            sage: P = posets.PentagonPoset()
-            sage: H = P._hasse_diagram
-            sage: H._backend.is_connected()
+            sage: P = posets.PentagonPoset()                                            # optional - sage.modules
+            sage: H = P._hasse_diagram                                                  # optional - sage.modules
+            sage: H._backend.is_connected()                                             # optional - sage.modules
             True
         """
         cdef int v_int
@@ -4589,9 +4589,9 @@ cdef class CGraphBackend(GenericGraphBackend):
 
         TESTS::
 
-            sage: m = Matrix(3,[0, 1, 1, 0, 0, 0, 0, 1, 0])
-            sage: g = DiGraph(m)
-            sage: g.is_directed_acyclic(certificate=True)
+            sage: m = Matrix(3,[0, 1, 1, 0, 0, 0, 0, 1, 0])                             # optional - sage.modules
+            sage: g = DiGraph(m)                                                        # optional - sage.modules
+            sage: g.is_directed_acyclic(certificate=True)                               # optional - sage.modules
             (True, [0, 2, 1])
         """
         if not self._directed:

src/sage/graphs/base/static_sparse_backend.pyx

@@ -446,17 +446,17 @@ cdef class StaticSparseBackend(CGraphBackend):
 
         ::
 
-            sage: g = DiGraph(digraphs.DeBruijn(4, 3), data_structure="static_sparse")
-            sage: gi = DiGraph(g, data_structure="static_sparse")
-            sage: gi.edges(sort=True)[0]
+            sage: g = DiGraph(digraphs.DeBruijn(4, 3), data_structure="static_sparse")  # optional - sage.combinat
+            sage: gi = DiGraph(g, data_structure="static_sparse")                       # optional - sage.combinat
+            sage: gi.edges(sort=True)[0]                                                # optional - sage.combinat
             ('000', '000', '0')
-            sage: sorted(gi.edges_incident('111'))
+            sage: sorted(gi.edges_incident('111'))                                      # optional - sage.combinat
             [('111', '110', '0'),
             ('111', '111', '1'),
             ('111', '112', '2'),
             ('111', '113', '3')]
 
-            sage: set(g.edges(sort=False)) == set(gi.edges(sort=False))
+            sage: set(g.edges(sort=False)) == set(gi.edges(sort=False))                 # optional - sage.combinat
             True
 
         ::
@@ -671,10 +671,10 @@ cdef class StaticSparseBackend(CGraphBackend):
         ::
 
             sage: from sage.graphs.base.static_sparse_backend import StaticSparseBackend
-            sage: g = StaticSparseBackend(digraphs.DeBruijn(3, 2))
-            sage: g.has_edge('00', '01', '1')
+            sage: g = StaticSparseBackend(digraphs.DeBruijn(3, 2))                      # optional - sage.combinat
+            sage: g.has_edge('00', '01', '1')                                           # optional - sage.combinat
             True
-            sage: g.has_edge('00', '01', '0')
+            sage: g.has_edge('00', '01', '0')                                           # optional - sage.combinat
             False
         """
         try: