two version of R2R are hereHEADmaster

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diff --git a/.venv/lib/python3.12/site-packages/networkx/generators/tests/test_classic.py b/.venv/lib/python3.12/site-packages/networkx/generators/tests/test_classic.py
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+"""
+====================
+Generators - Classic
+====================
+
+Unit tests for various classic graph generators in generators/classic.py
+"""
+
+import itertools
+import typing
+
+import pytest
+
+import networkx as nx
+from networkx.algorithms.isomorphism.isomorph import graph_could_be_isomorphic
+from networkx.utils import edges_equal, nodes_equal
+
+is_isomorphic = graph_could_be_isomorphic
+
+
+class TestGeneratorClassic:
+    def test_balanced_tree(self):
+        # balanced_tree(r,h) is a tree with (r**(h+1)-1)/(r-1) edges
+        for r, h in [(2, 2), (3, 3), (6, 2)]:
+            t = nx.balanced_tree(r, h)
+            order = t.order()
+            assert order == (r ** (h + 1) - 1) / (r - 1)
+            assert nx.is_connected(t)
+            assert t.size() == order - 1
+            dh = nx.degree_histogram(t)
+            assert dh[0] == 0  # no nodes of 0
+            assert dh[1] == r**h  # nodes of degree 1 are leaves
+            assert dh[r] == 1  # root is degree r
+            assert dh[r + 1] == order - r**h - 1  # everyone else is degree r+1
+            assert len(dh) == r + 2
+
+    def test_balanced_tree_star(self):
+        # balanced_tree(r,1) is the r-star
+        t = nx.balanced_tree(r=2, h=1)
+        assert is_isomorphic(t, nx.star_graph(2))
+        t = nx.balanced_tree(r=5, h=1)
+        assert is_isomorphic(t, nx.star_graph(5))
+        t = nx.balanced_tree(r=10, h=1)
+        assert is_isomorphic(t, nx.star_graph(10))
+
+    def test_balanced_tree_path(self):
+        """Tests that the balanced tree with branching factor one is the
+        path graph.
+
+        """
+        # A tree of height four has five levels.
+        T = nx.balanced_tree(1, 4)
+        P = nx.path_graph(5)
+        assert is_isomorphic(T, P)
+
+    def test_full_rary_tree(self):
+        r = 2
+        n = 9
+        t = nx.full_rary_tree(r, n)
+        assert t.order() == n
+        assert nx.is_connected(t)
+        dh = nx.degree_histogram(t)
+        assert dh[0] == 0  # no nodes of 0
+        assert dh[1] == 5  # nodes of degree 1 are leaves
+        assert dh[r] == 1  # root is degree r
+        assert dh[r + 1] == 9 - 5 - 1  # everyone else is degree r+1
+        assert len(dh) == r + 2
+
+    def test_full_rary_tree_balanced(self):
+        t = nx.full_rary_tree(2, 15)
+        th = nx.balanced_tree(2, 3)
+        assert is_isomorphic(t, th)
+
+    def test_full_rary_tree_path(self):
+        t = nx.full_rary_tree(1, 10)
+        assert is_isomorphic(t, nx.path_graph(10))
+
+    def test_full_rary_tree_empty(self):
+        t = nx.full_rary_tree(0, 10)
+        assert is_isomorphic(t, nx.empty_graph(10))
+        t = nx.full_rary_tree(3, 0)
+        assert is_isomorphic(t, nx.empty_graph(0))
+
+    def test_full_rary_tree_3_20(self):
+        t = nx.full_rary_tree(3, 20)
+        assert t.order() == 20
+
+    def test_barbell_graph(self):
+        # number of nodes = 2*m1 + m2 (2 m1-complete graphs + m2-path + 2 edges)
+        # number of edges = 2*(nx.number_of_edges(m1-complete graph) + m2 + 1
+        m1 = 3
+        m2 = 5
+        b = nx.barbell_graph(m1, m2)
+        assert nx.number_of_nodes(b) == 2 * m1 + m2
+        assert nx.number_of_edges(b) == m1 * (m1 - 1) + m2 + 1
+
+        m1 = 4
+        m2 = 10
+        b = nx.barbell_graph(m1, m2)
+        assert nx.number_of_nodes(b) == 2 * m1 + m2
+        assert nx.number_of_edges(b) == m1 * (m1 - 1) + m2 + 1
+
+        m1 = 3
+        m2 = 20
+        b = nx.barbell_graph(m1, m2)
+        assert nx.number_of_nodes(b) == 2 * m1 + m2
+        assert nx.number_of_edges(b) == m1 * (m1 - 1) + m2 + 1
+
+        # Raise NetworkXError if m1<2
+        m1 = 1
+        m2 = 20
+        pytest.raises(nx.NetworkXError, nx.barbell_graph, m1, m2)
+
+        # Raise NetworkXError if m2<0
+        m1 = 5
+        m2 = -2
+        pytest.raises(nx.NetworkXError, nx.barbell_graph, m1, m2)
+
+        # nx.barbell_graph(2,m) = nx.path_graph(m+4)
+        m1 = 2
+        m2 = 5
+        b = nx.barbell_graph(m1, m2)
+        assert is_isomorphic(b, nx.path_graph(m2 + 4))
+
+        m1 = 2
+        m2 = 10
+        b = nx.barbell_graph(m1, m2)
+        assert is_isomorphic(b, nx.path_graph(m2 + 4))
+
+        m1 = 2
+        m2 = 20
+        b = nx.barbell_graph(m1, m2)
+        assert is_isomorphic(b, nx.path_graph(m2 + 4))
+
+        pytest.raises(
+            nx.NetworkXError, nx.barbell_graph, m1, m2, create_using=nx.DiGraph()
+        )
+
+        mb = nx.barbell_graph(m1, m2, create_using=nx.MultiGraph())
+        assert edges_equal(mb.edges(), b.edges())
+
+    def test_binomial_tree(self):
+        graphs = (None, nx.Graph, nx.DiGraph, nx.MultiGraph, nx.MultiDiGraph)
+        for create_using in graphs:
+            for n in range(4):
+                b = nx.binomial_tree(n, create_using)
+                assert nx.number_of_nodes(b) == 2**n
+                assert nx.number_of_edges(b) == (2**n - 1)
+
+    def test_complete_graph(self):
+        # complete_graph(m) is a connected graph with
+        # m nodes and  m*(m+1)/2 edges
+        for m in [0, 1, 3, 5]:
+            g = nx.complete_graph(m)
+            assert nx.number_of_nodes(g) == m
+            assert nx.number_of_edges(g) == m * (m - 1) // 2
+
+        mg = nx.complete_graph(m, create_using=nx.MultiGraph)
+        assert edges_equal(mg.edges(), g.edges())
+
+        g = nx.complete_graph("abc")
+        assert nodes_equal(g.nodes(), ["a", "b", "c"])
+        assert g.size() == 3
+
+        # creates a self-loop... should it? <backward compatible says yes>
+        g = nx.complete_graph("abcb")
+        assert nodes_equal(g.nodes(), ["a", "b", "c"])
+        assert g.size() == 4
+
+        g = nx.complete_graph("abcb", create_using=nx.MultiGraph)
+        assert nodes_equal(g.nodes(), ["a", "b", "c"])
+        assert g.size() == 6
+
+    def test_complete_digraph(self):
+        # complete_graph(m) is a connected graph with
+        # m nodes and  m*(m+1)/2 edges
+        for m in [0, 1, 3, 5]:
+            g = nx.complete_graph(m, create_using=nx.DiGraph)
+            assert nx.number_of_nodes(g) == m
+            assert nx.number_of_edges(g) == m * (m - 1)
+
+        g = nx.complete_graph("abc", create_using=nx.DiGraph)
+        assert len(g) == 3
+        assert g.size() == 6
+        assert g.is_directed()
+
+    def test_circular_ladder_graph(self):
+        G = nx.circular_ladder_graph(5)
+        pytest.raises(
+            nx.NetworkXError, nx.circular_ladder_graph, 5, create_using=nx.DiGraph
+        )
+        mG = nx.circular_ladder_graph(5, create_using=nx.MultiGraph)
+        assert edges_equal(mG.edges(), G.edges())
+
+    def test_circulant_graph(self):
+        # Ci_n(1) is the cycle graph for all n
+        Ci6_1 = nx.circulant_graph(6, [1])
+        C6 = nx.cycle_graph(6)
+        assert edges_equal(Ci6_1.edges(), C6.edges())
+
+        # Ci_n(1, 2, ..., n div 2) is the complete graph for all n
+        Ci7 = nx.circulant_graph(7, [1, 2, 3])
+        K7 = nx.complete_graph(7)
+        assert edges_equal(Ci7.edges(), K7.edges())
+
+        # Ci_6(1, 3) is K_3,3 i.e. the utility graph
+        Ci6_1_3 = nx.circulant_graph(6, [1, 3])
+        K3_3 = nx.complete_bipartite_graph(3, 3)
+        assert is_isomorphic(Ci6_1_3, K3_3)
+
+    def test_cycle_graph(self):
+        G = nx.cycle_graph(4)
+        assert edges_equal(G.edges(), [(0, 1), (0, 3), (1, 2), (2, 3)])
+        mG = nx.cycle_graph(4, create_using=nx.MultiGraph)
+        assert edges_equal(mG.edges(), [(0, 1), (0, 3), (1, 2), (2, 3)])
+        G = nx.cycle_graph(4, create_using=nx.DiGraph)
+        assert not G.has_edge(2, 1)
+        assert G.has_edge(1, 2)
+        assert G.is_directed()
+
+        G = nx.cycle_graph("abc")
+        assert len(G) == 3
+        assert G.size() == 3
+        G = nx.cycle_graph("abcb")
+        assert len(G) == 3
+        assert G.size() == 2
+        g = nx.cycle_graph("abc", nx.DiGraph)
+        assert len(g) == 3
+        assert g.size() == 3
+        assert g.is_directed()
+        g = nx.cycle_graph("abcb", nx.DiGraph)
+        assert len(g) == 3
+        assert g.size() == 4
+
+    def test_dorogovtsev_goltsev_mendes_graph(self):
+        G = nx.dorogovtsev_goltsev_mendes_graph(0)
+        assert edges_equal(G.edges(), [(0, 1)])
+        assert nodes_equal(list(G), [0, 1])
+        G = nx.dorogovtsev_goltsev_mendes_graph(1)
+        assert edges_equal(G.edges(), [(0, 1), (0, 2), (1, 2)])
+        assert nx.average_clustering(G) == 1.0
+        assert nx.average_shortest_path_length(G) == 1.0
+        assert sorted(nx.triangles(G).values()) == [1, 1, 1]
+        assert nx.is_planar(G)
+        G = nx.dorogovtsev_goltsev_mendes_graph(2)
+        assert nx.number_of_nodes(G) == 6
+        assert nx.number_of_edges(G) == 9
+        assert nx.average_clustering(G) == 0.75
+        assert nx.average_shortest_path_length(G) == 1.4
+        assert nx.is_planar(G)
+        G = nx.dorogovtsev_goltsev_mendes_graph(10)
+        assert nx.number_of_nodes(G) == 29526
+        assert nx.number_of_edges(G) == 59049
+        assert G.degree(0) == 1024
+        assert G.degree(1) == 1024
+        assert G.degree(2) == 1024
+
+        with pytest.raises(nx.NetworkXError, match=r"n must be greater than"):
+            nx.dorogovtsev_goltsev_mendes_graph(-1)
+        with pytest.raises(nx.NetworkXError, match=r"directed graph not supported"):
+            nx.dorogovtsev_goltsev_mendes_graph(7, create_using=nx.DiGraph)
+        with pytest.raises(nx.NetworkXError, match=r"multigraph not supported"):
+            nx.dorogovtsev_goltsev_mendes_graph(7, create_using=nx.MultiGraph)
+        with pytest.raises(nx.NetworkXError):
+            nx.dorogovtsev_goltsev_mendes_graph(7, create_using=nx.MultiDiGraph)
+
+    def test_create_using(self):
+        G = nx.empty_graph()
+        assert isinstance(G, nx.Graph)
+        pytest.raises(TypeError, nx.empty_graph, create_using=0.0)
+        pytest.raises(TypeError, nx.empty_graph, create_using="Graph")
+
+        G = nx.empty_graph(create_using=nx.MultiGraph)
+        assert isinstance(G, nx.MultiGraph)
+        G = nx.empty_graph(create_using=nx.DiGraph)
+        assert isinstance(G, nx.DiGraph)
+
+        G = nx.empty_graph(create_using=nx.DiGraph, default=nx.MultiGraph)
+        assert isinstance(G, nx.DiGraph)
+        G = nx.empty_graph(create_using=None, default=nx.MultiGraph)
+        assert isinstance(G, nx.MultiGraph)
+        G = nx.empty_graph(default=nx.MultiGraph)
+        assert isinstance(G, nx.MultiGraph)
+
+        G = nx.path_graph(5)
+        H = nx.empty_graph(create_using=G)
+        assert not H.is_multigraph()
+        assert not H.is_directed()
+        assert len(H) == 0
+        assert G is H
+
+        H = nx.empty_graph(create_using=nx.MultiGraph())
+        assert H.is_multigraph()
+        assert not H.is_directed()
+        assert G is not H
+
+        # test for subclasses that also use typing.Protocol. See gh-6243
+        class Mixin(typing.Protocol):
+            pass
+
+        class MyGraph(Mixin, nx.DiGraph):
+            pass
+
+        G = nx.empty_graph(create_using=MyGraph)
+
+    def test_empty_graph(self):
+        G = nx.empty_graph()
+        assert nx.number_of_nodes(G) == 0
+        G = nx.empty_graph(42)
+        assert nx.number_of_nodes(G) == 42
+        assert nx.number_of_edges(G) == 0
+
+        G = nx.empty_graph("abc")
+        assert len(G) == 3
+        assert G.size() == 0
+
+        # create empty digraph
+        G = nx.empty_graph(42, create_using=nx.DiGraph(name="duh"))
+        assert nx.number_of_nodes(G) == 42
+        assert nx.number_of_edges(G) == 0
+        assert isinstance(G, nx.DiGraph)
+
+        # create empty multigraph
+        G = nx.empty_graph(42, create_using=nx.MultiGraph(name="duh"))
+        assert nx.number_of_nodes(G) == 42
+        assert nx.number_of_edges(G) == 0
+        assert isinstance(G, nx.MultiGraph)
+
+        # create empty graph from another
+        pete = nx.petersen_graph()
+        G = nx.empty_graph(42, create_using=pete)
+        assert nx.number_of_nodes(G) == 42
+        assert nx.number_of_edges(G) == 0
+        assert isinstance(G, nx.Graph)
+
+    def test_ladder_graph(self):
+        for i, G in [
+            (0, nx.empty_graph(0)),
+            (1, nx.path_graph(2)),
+            (2, nx.hypercube_graph(2)),
+            (10, nx.grid_graph([2, 10])),
+        ]:
+            assert is_isomorphic(nx.ladder_graph(i), G)
+
+        pytest.raises(nx.NetworkXError, nx.ladder_graph, 2, create_using=nx.DiGraph)
+
+        g = nx.ladder_graph(2)
+        mg = nx.ladder_graph(2, create_using=nx.MultiGraph)
+        assert edges_equal(mg.edges(), g.edges())
+
+    @pytest.mark.parametrize(("m", "n"), [(3, 5), (4, 10), (3, 20)])
+    def test_lollipop_graph_right_sizes(self, m, n):
+        G = nx.lollipop_graph(m, n)
+        assert nx.number_of_nodes(G) == m + n
+        assert nx.number_of_edges(G) == m * (m - 1) / 2 + n
+
+    @pytest.mark.parametrize(("m", "n"), [("ab", ""), ("abc", "defg")])
+    def test_lollipop_graph_size_node_sequence(self, m, n):
+        G = nx.lollipop_graph(m, n)
+        assert nx.number_of_nodes(G) == len(m) + len(n)
+        assert nx.number_of_edges(G) == len(m) * (len(m) - 1) / 2 + len(n)
+
+    def test_lollipop_graph_exceptions(self):
+        # Raise NetworkXError if m<2
+        pytest.raises(nx.NetworkXError, nx.lollipop_graph, -1, 2)
+        pytest.raises(nx.NetworkXError, nx.lollipop_graph, 1, 20)
+        pytest.raises(nx.NetworkXError, nx.lollipop_graph, "", 20)
+        pytest.raises(nx.NetworkXError, nx.lollipop_graph, "a", 20)
+
+        # Raise NetworkXError if n<0
+        pytest.raises(nx.NetworkXError, nx.lollipop_graph, 5, -2)
+
+        # raise NetworkXError if create_using is directed
+        with pytest.raises(nx.NetworkXError):
+            nx.lollipop_graph(2, 20, create_using=nx.DiGraph)
+        with pytest.raises(nx.NetworkXError):
+            nx.lollipop_graph(2, 20, create_using=nx.MultiDiGraph)
+
+    @pytest.mark.parametrize(("m", "n"), [(2, 0), (2, 5), (2, 10), ("ab", 20)])
+    def test_lollipop_graph_same_as_path_when_m1_is_2(self, m, n):
+        G = nx.lollipop_graph(m, n)
+        assert is_isomorphic(G, nx.path_graph(n + 2))
+
+    def test_lollipop_graph_for_multigraph(self):
+        G = nx.lollipop_graph(5, 20)
+        MG = nx.lollipop_graph(5, 20, create_using=nx.MultiGraph)
+        assert edges_equal(MG.edges(), G.edges())
+
+    @pytest.mark.parametrize(
+        ("m", "n"),
+        [(4, "abc"), ("abcd", 3), ([1, 2, 3, 4], "abc"), ("abcd", [1, 2, 3])],
+    )
+    def test_lollipop_graph_mixing_input_types(self, m, n):
+        expected = nx.compose(nx.complete_graph(4), nx.path_graph(range(100, 103)))
+        expected.add_edge(0, 100)  # Connect complete graph and path graph
+        assert is_isomorphic(nx.lollipop_graph(m, n), expected)
+
+    def test_lollipop_graph_non_builtin_ints(self):
+        np = pytest.importorskip("numpy")
+        G = nx.lollipop_graph(np.int32(4), np.int64(3))
+        expected = nx.compose(nx.complete_graph(4), nx.path_graph(range(100, 103)))
+        expected.add_edge(0, 100)  # Connect complete graph and path graph
+        assert is_isomorphic(G, expected)
+
+    def test_null_graph(self):
+        assert nx.number_of_nodes(nx.null_graph()) == 0
+
+    def test_path_graph(self):
+        p = nx.path_graph(0)
+        assert is_isomorphic(p, nx.null_graph())
+
+        p = nx.path_graph(1)
+        assert is_isomorphic(p, nx.empty_graph(1))
+
+        p = nx.path_graph(10)
+        assert nx.is_connected(p)
+        assert sorted(d for n, d in p.degree()) == [1, 1, 2, 2, 2, 2, 2, 2, 2, 2]
+        assert p.order() - 1 == p.size()
+
+        dp = nx.path_graph(3, create_using=nx.DiGraph)
+        assert dp.has_edge(0, 1)
+        assert not dp.has_edge(1, 0)
+
+        mp = nx.path_graph(10, create_using=nx.MultiGraph)
+        assert edges_equal(mp.edges(), p.edges())
+
+        G = nx.path_graph("abc")
+        assert len(G) == 3
+        assert G.size() == 2
+        G = nx.path_graph("abcb")
+        assert len(G) == 3
+        assert G.size() == 2
+        g = nx.path_graph("abc", nx.DiGraph)
+        assert len(g) == 3
+        assert g.size() == 2
+        assert g.is_directed()
+        g = nx.path_graph("abcb", nx.DiGraph)
+        assert len(g) == 3
+        assert g.size() == 3
+
+        G = nx.path_graph((1, 2, 3, 2, 4))
+        assert G.has_edge(2, 4)
+
+    def test_star_graph(self):
+        assert is_isomorphic(nx.star_graph(""), nx.empty_graph(0))
+        assert is_isomorphic(nx.star_graph([]), nx.empty_graph(0))
+        assert is_isomorphic(nx.star_graph(0), nx.empty_graph(1))
+        assert is_isomorphic(nx.star_graph(1), nx.path_graph(2))
+        assert is_isomorphic(nx.star_graph(2), nx.path_graph(3))
+        assert is_isomorphic(nx.star_graph(5), nx.complete_bipartite_graph(1, 5))
+
+        s = nx.star_graph(10)
+        assert sorted(d for n, d in s.degree()) == [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10]
+
+        pytest.raises(nx.NetworkXError, nx.star_graph, 10, create_using=nx.DiGraph)
+
+        ms = nx.star_graph(10, create_using=nx.MultiGraph)
+        assert edges_equal(ms.edges(), s.edges())
+
+        G = nx.star_graph("abc")
+        assert len(G) == 3
+        assert G.size() == 2
+
+        G = nx.star_graph("abcb")
+        assert len(G) == 3
+        assert G.size() == 2
+        G = nx.star_graph("abcb", create_using=nx.MultiGraph)
+        assert len(G) == 3
+        assert G.size() == 3
+
+        G = nx.star_graph("abcdefg")
+        assert len(G) == 7
+        assert G.size() == 6
+
+    def test_non_int_integers_for_star_graph(self):
+        np = pytest.importorskip("numpy")
+        G = nx.star_graph(np.int32(3))
+        assert len(G) == 4
+        assert G.size() == 3
+
+    @pytest.mark.parametrize(("m", "n"), [(3, 0), (3, 5), (4, 10), (3, 20)])
+    def test_tadpole_graph_right_sizes(self, m, n):
+        G = nx.tadpole_graph(m, n)
+        assert nx.number_of_nodes(G) == m + n
+        assert nx.number_of_edges(G) == m + n - (m == 2)
+
+    @pytest.mark.parametrize(("m", "n"), [("ab", ""), ("ab", "c"), ("abc", "defg")])
+    def test_tadpole_graph_size_node_sequences(self, m, n):
+        G = nx.tadpole_graph(m, n)
+        assert nx.number_of_nodes(G) == len(m) + len(n)
+        assert nx.number_of_edges(G) == len(m) + len(n) - (len(m) == 2)
+
+    def test_tadpole_graph_exceptions(self):
+        # Raise NetworkXError if m<2
+        pytest.raises(nx.NetworkXError, nx.tadpole_graph, -1, 3)
+        pytest.raises(nx.NetworkXError, nx.tadpole_graph, 0, 3)
+        pytest.raises(nx.NetworkXError, nx.tadpole_graph, 1, 3)
+
+        # Raise NetworkXError if n<0
+        pytest.raises(nx.NetworkXError, nx.tadpole_graph, 5, -2)
+
+        # Raise NetworkXError for digraphs
+        with pytest.raises(nx.NetworkXError):
+            nx.tadpole_graph(2, 20, create_using=nx.DiGraph)
+        with pytest.raises(nx.NetworkXError):
+            nx.tadpole_graph(2, 20, create_using=nx.MultiDiGraph)
+
+    @pytest.mark.parametrize(("m", "n"), [(2, 0), (2, 5), (2, 10), ("ab", 20)])
+    def test_tadpole_graph_same_as_path_when_m_is_2(self, m, n):
+        G = nx.tadpole_graph(m, n)
+        assert is_isomorphic(G, nx.path_graph(n + 2))
+
+    @pytest.mark.parametrize("m", [4, 7])
+    def test_tadpole_graph_same_as_cycle_when_m2_is_0(self, m):
+        G = nx.tadpole_graph(m, 0)
+        assert is_isomorphic(G, nx.cycle_graph(m))
+
+    def test_tadpole_graph_for_multigraph(self):
+        G = nx.tadpole_graph(5, 20)
+        MG = nx.tadpole_graph(5, 20, create_using=nx.MultiGraph)
+        assert edges_equal(MG.edges(), G.edges())
+
+    @pytest.mark.parametrize(
+        ("m", "n"),
+        [(4, "abc"), ("abcd", 3), ([1, 2, 3, 4], "abc"), ("abcd", [1, 2, 3])],
+    )
+    def test_tadpole_graph_mixing_input_types(self, m, n):
+        expected = nx.compose(nx.cycle_graph(4), nx.path_graph(range(100, 103)))
+        expected.add_edge(0, 100)  # Connect cycle and path
+        assert is_isomorphic(nx.tadpole_graph(m, n), expected)
+
+    def test_tadpole_graph_non_builtin_integers(self):
+        np = pytest.importorskip("numpy")
+        G = nx.tadpole_graph(np.int32(4), np.int64(3))
+        expected = nx.compose(nx.cycle_graph(4), nx.path_graph(range(100, 103)))
+        expected.add_edge(0, 100)  # Connect cycle and path
+        assert is_isomorphic(G, expected)
+
+    def test_trivial_graph(self):
+        assert nx.number_of_nodes(nx.trivial_graph()) == 1
+
+    def test_turan_graph(self):
+        assert nx.number_of_edges(nx.turan_graph(13, 4)) == 63
+        assert is_isomorphic(
+            nx.turan_graph(13, 4), nx.complete_multipartite_graph(3, 4, 3, 3)
+        )
+
+    def test_wheel_graph(self):
+        for n, G in [
+            ("", nx.null_graph()),
+            (0, nx.null_graph()),
+            (1, nx.empty_graph(1)),
+            (2, nx.path_graph(2)),
+            (3, nx.complete_graph(3)),
+            (4, nx.complete_graph(4)),
+        ]:
+            g = nx.wheel_graph(n)
+            assert is_isomorphic(g, G)
+
+        g = nx.wheel_graph(10)
+        assert sorted(d for n, d in g.degree()) == [3, 3, 3, 3, 3, 3, 3, 3, 3, 9]
+
+        pytest.raises(nx.NetworkXError, nx.wheel_graph, 10, create_using=nx.DiGraph)
+
+        mg = nx.wheel_graph(10, create_using=nx.MultiGraph())
+        assert edges_equal(mg.edges(), g.edges())
+
+        G = nx.wheel_graph("abc")
+        assert len(G) == 3
+        assert G.size() == 3
+
+        G = nx.wheel_graph("abcb")
+        assert len(G) == 3
+        assert G.size() == 4
+        G = nx.wheel_graph("abcb", nx.MultiGraph)
+        assert len(G) == 3
+        assert G.size() == 6
+
+    def test_non_int_integers_for_wheel_graph(self):
+        np = pytest.importorskip("numpy")
+        G = nx.wheel_graph(np.int32(3))
+        assert len(G) == 3
+        assert G.size() == 3
+
+    def test_complete_0_partite_graph(self):
+        """Tests that the complete 0-partite graph is the null graph."""
+        G = nx.complete_multipartite_graph()
+        H = nx.null_graph()
+        assert nodes_equal(G, H)
+        assert edges_equal(G.edges(), H.edges())
+
+    def test_complete_1_partite_graph(self):
+        """Tests that the complete 1-partite graph is the empty graph."""
+        G = nx.complete_multipartite_graph(3)
+        H = nx.empty_graph(3)
+        assert nodes_equal(G, H)
+        assert edges_equal(G.edges(), H.edges())
+
+    def test_complete_2_partite_graph(self):
+        """Tests that the complete 2-partite graph is the complete bipartite
+        graph.
+
+        """
+        G = nx.complete_multipartite_graph(2, 3)
+        H = nx.complete_bipartite_graph(2, 3)
+        assert nodes_equal(G, H)
+        assert edges_equal(G.edges(), H.edges())
+
+    def test_complete_multipartite_graph(self):
+        """Tests for generating the complete multipartite graph."""
+        G = nx.complete_multipartite_graph(2, 3, 4)
+        blocks = [(0, 1), (2, 3, 4), (5, 6, 7, 8)]
+        # Within each block, no two vertices should be adjacent.
+        for block in blocks:
+            for u, v in itertools.combinations_with_replacement(block, 2):
+                assert v not in G[u]
+                assert G.nodes[u] == G.nodes[v]
+        # Across blocks, all vertices should be adjacent.
+        for block1, block2 in itertools.combinations(blocks, 2):
+            for u, v in itertools.product(block1, block2):
+                assert v in G[u]
+                assert G.nodes[u] != G.nodes[v]
+        with pytest.raises(nx.NetworkXError, match="Negative number of nodes"):
+            nx.complete_multipartite_graph(2, -3, 4)
+
+    def test_kneser_graph(self):
+        # the petersen graph is a special case of the kneser graph when n=5 and k=2
+        assert is_isomorphic(nx.kneser_graph(5, 2), nx.petersen_graph())
+
+        # when k is 1, the kneser graph returns a complete graph with n vertices
+        for i in range(1, 7):
+            assert is_isomorphic(nx.kneser_graph(i, 1), nx.complete_graph(i))
+
+        # the kneser graph of n and n-1 is the empty graph with n vertices
+        for j in range(3, 7):
+            assert is_isomorphic(nx.kneser_graph(j, j - 1), nx.empty_graph(j))
+
+        # in general the number of edges of the kneser graph is equal to
+        # (n choose k) times (n-k choose k) divided by 2
+        assert nx.number_of_edges(nx.kneser_graph(8, 3)) == 280