two version of R2R are here HEAD master

1 files changed, 835 insertions, 0 deletions

diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/tests/test_dag.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/tests/test_dag.py
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+from collections import deque
+from itertools import combinations, permutations
+
+import pytest
+
+import networkx as nx
+from networkx.utils import edges_equal, pairwise
+
+
+# Recipe from the itertools documentation.
+def _consume(iterator):
+    "Consume the iterator entirely."
+    # Feed the entire iterator into a zero-length deque.
+    deque(iterator, maxlen=0)
+
+
+class TestDagLongestPath:
+    """Unit tests computing the longest path in a directed acyclic graph."""
+
+    def test_empty(self):
+        G = nx.DiGraph()
+        assert nx.dag_longest_path(G) == []
+
+    def test_unweighted1(self):
+        edges = [(1, 2), (2, 3), (2, 4), (3, 5), (5, 6), (3, 7)]
+        G = nx.DiGraph(edges)
+        assert nx.dag_longest_path(G) == [1, 2, 3, 5, 6]
+
+    def test_unweighted2(self):
+        edges = [(1, 2), (2, 3), (3, 4), (4, 5), (1, 3), (1, 5), (3, 5)]
+        G = nx.DiGraph(edges)
+        assert nx.dag_longest_path(G) == [1, 2, 3, 4, 5]
+
+    def test_weighted(self):
+        G = nx.DiGraph()
+        edges = [(1, 2, -5), (2, 3, 1), (3, 4, 1), (4, 5, 0), (3, 5, 4), (1, 6, 2)]
+        G.add_weighted_edges_from(edges)
+        assert nx.dag_longest_path(G) == [2, 3, 5]
+
+    def test_undirected_not_implemented(self):
+        G = nx.Graph()
+        pytest.raises(nx.NetworkXNotImplemented, nx.dag_longest_path, G)
+
+    def test_unorderable_nodes(self):
+        """Tests that computing the longest path does not depend on
+        nodes being orderable.
+
+        For more information, see issue #1989.
+
+        """
+        # Create the directed path graph on four nodes in a diamond shape,
+        # with nodes represented as (unorderable) Python objects.
+        nodes = [object() for n in range(4)]
+        G = nx.DiGraph()
+        G.add_edge(nodes[0], nodes[1])
+        G.add_edge(nodes[0], nodes[2])
+        G.add_edge(nodes[2], nodes[3])
+        G.add_edge(nodes[1], nodes[3])
+
+        # this will raise NotImplementedError when nodes need to be ordered
+        nx.dag_longest_path(G)
+
+    def test_multigraph_unweighted(self):
+        edges = [(1, 2), (2, 3), (2, 3), (3, 4), (4, 5), (1, 3), (1, 5), (3, 5)]
+        G = nx.MultiDiGraph(edges)
+        assert nx.dag_longest_path(G) == [1, 2, 3, 4, 5]
+
+    def test_multigraph_weighted(self):
+        G = nx.MultiDiGraph()
+        edges = [
+            (1, 2, 2),
+            (2, 3, 2),
+            (1, 3, 1),
+            (1, 3, 5),
+            (1, 3, 2),
+        ]
+        G.add_weighted_edges_from(edges)
+        assert nx.dag_longest_path(G) == [1, 3]
+
+    def test_multigraph_weighted_default_weight(self):
+        G = nx.MultiDiGraph([(1, 2), (2, 3)])  # Unweighted edges
+        G.add_weighted_edges_from([(1, 3, 1), (1, 3, 5), (1, 3, 2)])
+
+        # Default value for default weight is 1
+        assert nx.dag_longest_path(G) == [1, 3]
+        assert nx.dag_longest_path(G, default_weight=3) == [1, 2, 3]
+
+
+class TestDagLongestPathLength:
+    """Unit tests for computing the length of a longest path in a
+    directed acyclic graph.
+
+    """
+
+    def test_unweighted(self):
+        edges = [(1, 2), (2, 3), (2, 4), (3, 5), (5, 6), (5, 7)]
+        G = nx.DiGraph(edges)
+        assert nx.dag_longest_path_length(G) == 4
+
+        edges = [(1, 2), (2, 3), (3, 4), (4, 5), (1, 3), (1, 5), (3, 5)]
+        G = nx.DiGraph(edges)
+        assert nx.dag_longest_path_length(G) == 4
+
+        # test degenerate graphs
+        G = nx.DiGraph()
+        G.add_node(1)
+        assert nx.dag_longest_path_length(G) == 0
+
+    def test_undirected_not_implemented(self):
+        G = nx.Graph()
+        pytest.raises(nx.NetworkXNotImplemented, nx.dag_longest_path_length, G)
+
+    def test_weighted(self):
+        edges = [(1, 2, -5), (2, 3, 1), (3, 4, 1), (4, 5, 0), (3, 5, 4), (1, 6, 2)]
+        G = nx.DiGraph()
+        G.add_weighted_edges_from(edges)
+        assert nx.dag_longest_path_length(G) == 5
+
+    def test_multigraph_unweighted(self):
+        edges = [(1, 2), (2, 3), (2, 3), (3, 4), (4, 5), (1, 3), (1, 5), (3, 5)]
+        G = nx.MultiDiGraph(edges)
+        assert nx.dag_longest_path_length(G) == 4
+
+    def test_multigraph_weighted(self):
+        G = nx.MultiDiGraph()
+        edges = [
+            (1, 2, 2),
+            (2, 3, 2),
+            (1, 3, 1),
+            (1, 3, 5),
+            (1, 3, 2),
+        ]
+        G.add_weighted_edges_from(edges)
+        assert nx.dag_longest_path_length(G) == 5
+
+
+class TestDAG:
+    @classmethod
+    def setup_class(cls):
+        pass
+
+    def test_topological_sort1(self):
+        DG = nx.DiGraph([(1, 2), (1, 3), (2, 3)])
+
+        for algorithm in [nx.topological_sort, nx.lexicographical_topological_sort]:
+            assert tuple(algorithm(DG)) == (1, 2, 3)
+
+        DG.add_edge(3, 2)
+
+        for algorithm in [nx.topological_sort, nx.lexicographical_topological_sort]:
+            pytest.raises(nx.NetworkXUnfeasible, _consume, algorithm(DG))
+
+        DG.remove_edge(2, 3)
+
+        for algorithm in [nx.topological_sort, nx.lexicographical_topological_sort]:
+            assert tuple(algorithm(DG)) == (1, 3, 2)
+
+        DG.remove_edge(3, 2)
+
+        assert tuple(nx.topological_sort(DG)) in {(1, 2, 3), (1, 3, 2)}
+        assert tuple(nx.lexicographical_topological_sort(DG)) == (1, 2, 3)
+
+    def test_is_directed_acyclic_graph(self):
+        G = nx.generators.complete_graph(2)
+        assert not nx.is_directed_acyclic_graph(G)
+        assert not nx.is_directed_acyclic_graph(G.to_directed())
+        assert not nx.is_directed_acyclic_graph(nx.Graph([(3, 4), (4, 5)]))
+        assert nx.is_directed_acyclic_graph(nx.DiGraph([(3, 4), (4, 5)]))
+
+    def test_topological_sort2(self):
+        DG = nx.DiGraph(
+            {
+                1: [2],
+                2: [3],
+                3: [4],
+                4: [5],
+                5: [1],
+                11: [12],
+                12: [13],
+                13: [14],
+                14: [15],
+            }
+        )
+        pytest.raises(nx.NetworkXUnfeasible, _consume, nx.topological_sort(DG))
+
+        assert not nx.is_directed_acyclic_graph(DG)
+
+        DG.remove_edge(1, 2)
+        _consume(nx.topological_sort(DG))
+        assert nx.is_directed_acyclic_graph(DG)
+
+    def test_topological_sort3(self):
+        DG = nx.DiGraph()
+        DG.add_edges_from([(1, i) for i in range(2, 5)])
+        DG.add_edges_from([(2, i) for i in range(5, 9)])
+        DG.add_edges_from([(6, i) for i in range(9, 12)])
+        DG.add_edges_from([(4, i) for i in range(12, 15)])
+
+        def validate(order):
+            assert isinstance(order, list)
+            assert set(order) == set(DG)
+            for u, v in combinations(order, 2):
+                assert not nx.has_path(DG, v, u)
+
+        validate(list(nx.topological_sort(DG)))
+
+        DG.add_edge(14, 1)
+        pytest.raises(nx.NetworkXUnfeasible, _consume, nx.topological_sort(DG))
+
+    def test_topological_sort4(self):
+        G = nx.Graph()
+        G.add_edge(1, 2)
+        # Only directed graphs can be topologically sorted.
+        pytest.raises(nx.NetworkXError, _consume, nx.topological_sort(G))
+
+    def test_topological_sort5(self):
+        G = nx.DiGraph()
+        G.add_edge(0, 1)
+        assert list(nx.topological_sort(G)) == [0, 1]
+
+    def test_topological_sort6(self):
+        for algorithm in [nx.topological_sort, nx.lexicographical_topological_sort]:
+
+            def runtime_error():
+                DG = nx.DiGraph([(1, 2), (2, 3), (3, 4)])
+                first = True
+                for x in algorithm(DG):
+                    if first:
+                        first = False
+                        DG.add_edge(5 - x, 5)
+
+            def unfeasible_error():
+                DG = nx.DiGraph([(1, 2), (2, 3), (3, 4)])
+                first = True
+                for x in algorithm(DG):
+                    if first:
+                        first = False
+                        DG.remove_node(4)
+
+            def runtime_error2():
+                DG = nx.DiGraph([(1, 2), (2, 3), (3, 4)])
+                first = True
+                for x in algorithm(DG):
+                    if first:
+                        first = False
+                        DG.remove_node(2)
+
+            pytest.raises(RuntimeError, runtime_error)
+            pytest.raises(RuntimeError, runtime_error2)
+            pytest.raises(nx.NetworkXUnfeasible, unfeasible_error)
+
+    def test_all_topological_sorts_1(self):
+        DG = nx.DiGraph([(1, 2), (2, 3), (3, 4), (4, 5)])
+        assert list(nx.all_topological_sorts(DG)) == [[1, 2, 3, 4, 5]]
+
+    def test_all_topological_sorts_2(self):
+        DG = nx.DiGraph([(1, 3), (2, 1), (2, 4), (4, 3), (4, 5)])
+        assert sorted(nx.all_topological_sorts(DG)) == [
+            [2, 1, 4, 3, 5],
+            [2, 1, 4, 5, 3],
+            [2, 4, 1, 3, 5],
+            [2, 4, 1, 5, 3],
+            [2, 4, 5, 1, 3],
+        ]
+
+    def test_all_topological_sorts_3(self):
+        def unfeasible():
+            DG = nx.DiGraph([(1, 2), (2, 3), (3, 4), (4, 2), (4, 5)])
+            # convert to list to execute generator
+            list(nx.all_topological_sorts(DG))
+
+        def not_implemented():
+            G = nx.Graph([(1, 2), (2, 3)])
+            # convert to list to execute generator
+            list(nx.all_topological_sorts(G))
+
+        def not_implemented_2():
+            G = nx.MultiGraph([(1, 2), (1, 2), (2, 3)])
+            list(nx.all_topological_sorts(G))
+
+        pytest.raises(nx.NetworkXUnfeasible, unfeasible)
+        pytest.raises(nx.NetworkXNotImplemented, not_implemented)
+        pytest.raises(nx.NetworkXNotImplemented, not_implemented_2)
+
+    def test_all_topological_sorts_4(self):
+        DG = nx.DiGraph()
+        for i in range(7):
+            DG.add_node(i)
+        assert sorted(map(list, permutations(DG.nodes))) == sorted(
+            nx.all_topological_sorts(DG)
+        )
+
+    def test_all_topological_sorts_multigraph_1(self):
+        DG = nx.MultiDiGraph([(1, 2), (1, 2), (2, 3), (3, 4), (3, 5), (3, 5), (3, 5)])
+        assert sorted(nx.all_topological_sorts(DG)) == sorted(
+            [[1, 2, 3, 4, 5], [1, 2, 3, 5, 4]]
+        )
+
+    def test_all_topological_sorts_multigraph_2(self):
+        N = 9
+        edges = []
+        for i in range(1, N):
+            edges.extend([(i, i + 1)] * i)
+        DG = nx.MultiDiGraph(edges)
+        assert list(nx.all_topological_sorts(DG)) == [list(range(1, N + 1))]
+
+    def test_ancestors(self):
+        G = nx.DiGraph()
+        ancestors = nx.algorithms.dag.ancestors
+        G.add_edges_from([(1, 2), (1, 3), (4, 2), (4, 3), (4, 5), (2, 6), (5, 6)])
+        assert ancestors(G, 6) == {1, 2, 4, 5}
+        assert ancestors(G, 3) == {1, 4}
+        assert ancestors(G, 1) == set()
+        pytest.raises(nx.NetworkXError, ancestors, G, 8)
+
+    def test_descendants(self):
+        G = nx.DiGraph()
+        descendants = nx.algorithms.dag.descendants
+        G.add_edges_from([(1, 2), (1, 3), (4, 2), (4, 3), (4, 5), (2, 6), (5, 6)])
+        assert descendants(G, 1) == {2, 3, 6}
+        assert descendants(G, 4) == {2, 3, 5, 6}
+        assert descendants(G, 3) == set()
+        pytest.raises(nx.NetworkXError, descendants, G, 8)
+
+    def test_transitive_closure(self):
+        G = nx.DiGraph([(1, 2), (2, 3), (3, 4)])
+        solution = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
+        assert edges_equal(nx.transitive_closure(G).edges(), solution)
+        G = nx.DiGraph([(1, 2), (2, 3), (2, 4)])
+        solution = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4)]
+        assert edges_equal(nx.transitive_closure(G).edges(), solution)
+        G = nx.DiGraph([(1, 2), (2, 3), (3, 1)])
+        solution = [(1, 2), (2, 1), (2, 3), (3, 2), (1, 3), (3, 1)]
+        soln = sorted(solution + [(n, n) for n in G])
+        assert edges_equal(sorted(nx.transitive_closure(G).edges()), soln)
+
+        G = nx.Graph([(1, 2), (2, 3), (3, 4)])
+        solution = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
+        assert edges_equal(sorted(nx.transitive_closure(G).edges()), solution)
+
+        G = nx.MultiGraph([(1, 2), (2, 3), (3, 4)])
+        solution = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
+        assert edges_equal(sorted(nx.transitive_closure(G).edges()), solution)
+
+        G = nx.MultiDiGraph([(1, 2), (2, 3), (3, 4)])
+        solution = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
+        assert edges_equal(sorted(nx.transitive_closure(G).edges()), solution)
+
+        # test if edge data is copied
+        G = nx.DiGraph([(1, 2, {"a": 3}), (2, 3, {"b": 0}), (3, 4)])
+        H = nx.transitive_closure(G)
+        for u, v in G.edges():
+            assert G.get_edge_data(u, v) == H.get_edge_data(u, v)
+
+        k = 10
+        G = nx.DiGraph((i, i + 1, {"f": "b", "weight": i}) for i in range(k))
+        H = nx.transitive_closure(G)
+        for u, v in G.edges():
+            assert G.get_edge_data(u, v) == H.get_edge_data(u, v)
+
+        G = nx.Graph()
+        with pytest.raises(nx.NetworkXError):
+            nx.transitive_closure(G, reflexive="wrong input")
+
+    def test_reflexive_transitive_closure(self):
+        G = nx.DiGraph([(1, 2), (2, 3), (3, 4)])
+        solution = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
+        soln = sorted(solution + [(n, n) for n in G])
+        assert edges_equal(nx.transitive_closure(G).edges(), solution)
+        assert edges_equal(nx.transitive_closure(G, False).edges(), solution)
+        assert edges_equal(nx.transitive_closure(G, True).edges(), soln)
+        assert edges_equal(nx.transitive_closure(G, None).edges(), solution)
+
+        G = nx.DiGraph([(1, 2), (2, 3), (2, 4)])
+        solution = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4)]
+        soln = sorted(solution + [(n, n) for n in G])
+        assert edges_equal(nx.transitive_closure(G).edges(), solution)
+        assert edges_equal(nx.transitive_closure(G, False).edges(), solution)
+        assert edges_equal(nx.transitive_closure(G, True).edges(), soln)
+        assert edges_equal(nx.transitive_closure(G, None).edges(), solution)
+
+        G = nx.DiGraph([(1, 2), (2, 3), (3, 1)])
+        solution = sorted([(1, 2), (2, 1), (2, 3), (3, 2), (1, 3), (3, 1)])
+        soln = sorted(solution + [(n, n) for n in G])
+        assert edges_equal(sorted(nx.transitive_closure(G).edges()), soln)
+        assert edges_equal(sorted(nx.transitive_closure(G, False).edges()), soln)
+        assert edges_equal(sorted(nx.transitive_closure(G, None).edges()), solution)
+        assert edges_equal(sorted(nx.transitive_closure(G, True).edges()), soln)
+
+        G = nx.Graph([(1, 2), (2, 3), (3, 4)])
+        solution = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
+        soln = sorted(solution + [(n, n) for n in G])
+        assert edges_equal(nx.transitive_closure(G).edges(), solution)
+        assert edges_equal(nx.transitive_closure(G, False).edges(), solution)
+        assert edges_equal(nx.transitive_closure(G, True).edges(), soln)
+        assert edges_equal(nx.transitive_closure(G, None).edges(), solution)
+
+        G = nx.MultiGraph([(1, 2), (2, 3), (3, 4)])
+        solution = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
+        soln = sorted(solution + [(n, n) for n in G])
+        assert edges_equal(nx.transitive_closure(G).edges(), solution)
+        assert edges_equal(nx.transitive_closure(G, False).edges(), solution)
+        assert edges_equal(nx.transitive_closure(G, True).edges(), soln)
+        assert edges_equal(nx.transitive_closure(G, None).edges(), solution)
+
+        G = nx.MultiDiGraph([(1, 2), (2, 3), (3, 4)])
+        solution = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
+        soln = sorted(solution + [(n, n) for n in G])
+        assert edges_equal(nx.transitive_closure(G).edges(), solution)
+        assert edges_equal(nx.transitive_closure(G, False).edges(), solution)
+        assert edges_equal(nx.transitive_closure(G, True).edges(), soln)
+        assert edges_equal(nx.transitive_closure(G, None).edges(), solution)
+
+    def test_transitive_closure_dag(self):
+        G = nx.DiGraph([(1, 2), (2, 3), (3, 4)])
+        transitive_closure = nx.algorithms.dag.transitive_closure_dag
+        solution = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
+        assert edges_equal(transitive_closure(G).edges(), solution)
+        G = nx.DiGraph([(1, 2), (2, 3), (2, 4)])
+        solution = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4)]
+        assert edges_equal(transitive_closure(G).edges(), solution)
+        G = nx.Graph([(1, 2), (2, 3), (3, 4)])
+        pytest.raises(nx.NetworkXNotImplemented, transitive_closure, G)
+
+        # test if edge data is copied
+        G = nx.DiGraph([(1, 2, {"a": 3}), (2, 3, {"b": 0}), (3, 4)])
+        H = transitive_closure(G)
+        for u, v in G.edges():
+            assert G.get_edge_data(u, v) == H.get_edge_data(u, v)
+
+        k = 10
+        G = nx.DiGraph((i, i + 1, {"foo": "bar", "weight": i}) for i in range(k))
+        H = transitive_closure(G)
+        for u, v in G.edges():
+            assert G.get_edge_data(u, v) == H.get_edge_data(u, v)
+
+    def test_transitive_reduction(self):
+        G = nx.DiGraph([(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)])
+        transitive_reduction = nx.algorithms.dag.transitive_reduction
+        solution = [(1, 2), (2, 3), (3, 4)]
+        assert edges_equal(transitive_reduction(G).edges(), solution)
+        G = nx.DiGraph([(1, 2), (1, 3), (1, 4), (2, 3), (2, 4)])
+        transitive_reduction = nx.algorithms.dag.transitive_reduction
+        solution = [(1, 2), (2, 3), (2, 4)]
+        assert edges_equal(transitive_reduction(G).edges(), solution)
+        G = nx.Graph([(1, 2), (2, 3), (3, 4)])
+        pytest.raises(nx.NetworkXNotImplemented, transitive_reduction, G)
+
+    def _check_antichains(self, solution, result):
+        sol = [frozenset(a) for a in solution]
+        res = [frozenset(a) for a in result]
+        assert set(sol) == set(res)
+
+    def test_antichains(self):
+        antichains = nx.algorithms.dag.antichains
+        G = nx.DiGraph([(1, 2), (2, 3), (3, 4)])
+        solution = [[], [4], [3], [2], [1]]
+        self._check_antichains(list(antichains(G)), solution)
+        G = nx.DiGraph([(1, 2), (2, 3), (2, 4), (3, 5), (5, 6), (5, 7)])
+        solution = [
+            [],
+            [4],
+            [7],
+            [7, 4],
+            [6],
+            [6, 4],
+            [6, 7],
+            [6, 7, 4],
+            [5],
+            [5, 4],
+            [3],
+            [3, 4],
+            [2],
+            [1],
+        ]
+        self._check_antichains(list(antichains(G)), solution)
+        G = nx.DiGraph([(1, 2), (1, 3), (3, 4), (3, 5), (5, 6)])
+        solution = [
+            [],
+            [6],
+            [5],
+            [4],
+            [4, 6],
+            [4, 5],
+            [3],
+            [2],
+            [2, 6],
+            [2, 5],
+            [2, 4],
+            [2, 4, 6],
+            [2, 4, 5],
+            [2, 3],
+            [1],
+        ]
+        self._check_antichains(list(antichains(G)), solution)
+        G = nx.DiGraph({0: [1, 2], 1: [4], 2: [3], 3: [4]})
+        solution = [[], [4], [3], [2], [1], [1, 3], [1, 2], [0]]
+        self._check_antichains(list(antichains(G)), solution)
+        G = nx.DiGraph()
+        self._check_antichains(list(antichains(G)), [[]])
+        G = nx.DiGraph()
+        G.add_nodes_from([0, 1, 2])
+        solution = [[], [0], [1], [1, 0], [2], [2, 0], [2, 1], [2, 1, 0]]
+        self._check_antichains(list(antichains(G)), solution)
+
+        def f(x):
+            return list(antichains(x))
+
+        G = nx.Graph([(1, 2), (2, 3), (3, 4)])
+        pytest.raises(nx.NetworkXNotImplemented, f, G)
+        G = nx.DiGraph([(1, 2), (2, 3), (3, 1)])
+        pytest.raises(nx.NetworkXUnfeasible, f, G)
+
+    def test_lexicographical_topological_sort(self):
+        G = nx.DiGraph([(1, 2), (2, 3), (1, 4), (1, 5), (2, 6)])
+        assert list(nx.lexicographical_topological_sort(G)) == [1, 2, 3, 4, 5, 6]
+        assert list(nx.lexicographical_topological_sort(G, key=lambda x: x)) == [
+            1,
+            2,
+            3,
+            4,
+            5,
+            6,
+        ]
+        assert list(nx.lexicographical_topological_sort(G, key=lambda x: -x)) == [
+            1,
+            5,
+            4,
+            2,
+            6,
+            3,
+        ]
+
+    def test_lexicographical_topological_sort2(self):
+        """
+        Check the case of two or more nodes with same key value.
+        Want to avoid exception raised due to comparing nodes directly.
+        See Issue #3493
+        """
+
+        class Test_Node:
+            def __init__(self, n):
+                self.label = n
+                self.priority = 1
+
+            def __repr__(self):
+                return f"Node({self.label})"
+
+        def sorting_key(node):
+            return node.priority
+
+        test_nodes = [Test_Node(n) for n in range(4)]
+        G = nx.DiGraph()
+        edges = [(0, 1), (0, 2), (0, 3), (2, 3)]
+        G.add_edges_from((test_nodes[a], test_nodes[b]) for a, b in edges)
+
+        sorting = list(nx.lexicographical_topological_sort(G, key=sorting_key))
+        assert sorting == test_nodes
+
+
+def test_topological_generations():
+    G = nx.DiGraph(
+        {1: [2, 3], 2: [4, 5], 3: [7], 4: [], 5: [6, 7], 6: [], 7: []}
+    ).reverse()
+    # order within each generation is inconsequential
+    generations = [sorted(gen) for gen in nx.topological_generations(G)]
+    expected = [[4, 6, 7], [3, 5], [2], [1]]
+    assert generations == expected
+
+    MG = nx.MultiDiGraph(G.edges)
+    MG.add_edge(2, 1)
+    generations = [sorted(gen) for gen in nx.topological_generations(MG)]
+    assert generations == expected
+
+
+def test_topological_generations_empty():
+    G = nx.DiGraph()
+    assert list(nx.topological_generations(G)) == []
+
+
+def test_topological_generations_cycle():
+    G = nx.DiGraph([[2, 1], [3, 1], [1, 2]])
+    with pytest.raises(nx.NetworkXUnfeasible):
+        list(nx.topological_generations(G))
+
+
+def test_is_aperiodic_cycle():
+    G = nx.DiGraph()
+    nx.add_cycle(G, [1, 2, 3, 4])
+    assert not nx.is_aperiodic(G)
+
+
+def test_is_aperiodic_cycle2():
+    G = nx.DiGraph()
+    nx.add_cycle(G, [1, 2, 3, 4])
+    nx.add_cycle(G, [3, 4, 5, 6, 7])
+    assert nx.is_aperiodic(G)
+
+
+def test_is_aperiodic_cycle3():
+    G = nx.DiGraph()
+    nx.add_cycle(G, [1, 2, 3, 4])
+    nx.add_cycle(G, [3, 4, 5, 6])
+    assert not nx.is_aperiodic(G)
+
+
+def test_is_aperiodic_cycle4():
+    G = nx.DiGraph()
+    nx.add_cycle(G, [1, 2, 3, 4])
+    G.add_edge(1, 3)
+    assert nx.is_aperiodic(G)
+
+
+def test_is_aperiodic_selfloop():
+    G = nx.DiGraph()
+    nx.add_cycle(G, [1, 2, 3, 4])
+    G.add_edge(1, 1)
+    assert nx.is_aperiodic(G)
+
+
+def test_is_aperiodic_undirected_raises():
+    G = nx.Graph()
+    pytest.raises(nx.NetworkXError, nx.is_aperiodic, G)
+
+
+def test_is_aperiodic_empty_graph():
+    G = nx.empty_graph(create_using=nx.DiGraph)
+    with pytest.raises(nx.NetworkXPointlessConcept, match="Graph has no nodes."):
+        nx.is_aperiodic(G)
+
+
+def test_is_aperiodic_bipartite():
+    # Bipartite graph
+    G = nx.DiGraph(nx.davis_southern_women_graph())
+    assert not nx.is_aperiodic(G)
+
+
+def test_is_aperiodic_rary_tree():
+    G = nx.full_rary_tree(3, 27, create_using=nx.DiGraph())
+    assert not nx.is_aperiodic(G)
+
+
+def test_is_aperiodic_disconnected():
+    # disconnected graph
+    G = nx.DiGraph()
+    nx.add_cycle(G, [1, 2, 3, 4])
+    nx.add_cycle(G, [5, 6, 7, 8])
+    assert not nx.is_aperiodic(G)
+    G.add_edge(1, 3)
+    G.add_edge(5, 7)
+    assert nx.is_aperiodic(G)
+
+
+def test_is_aperiodic_disconnected2():
+    G = nx.DiGraph()
+    nx.add_cycle(G, [0, 1, 2])
+    G.add_edge(3, 3)
+    assert not nx.is_aperiodic(G)
+
+
+class TestDagToBranching:
+    """Unit tests for the :func:`networkx.dag_to_branching` function."""
+
+    def test_single_root(self):
+        """Tests that a directed acyclic graph with a single degree
+        zero node produces an arborescence.
+
+        """
+        G = nx.DiGraph([(0, 1), (0, 2), (1, 3), (2, 3)])
+        B = nx.dag_to_branching(G)
+        expected = nx.DiGraph([(0, 1), (1, 3), (0, 2), (2, 4)])
+        assert nx.is_arborescence(B)
+        assert nx.is_isomorphic(B, expected)
+
+    def test_multiple_roots(self):
+        """Tests that a directed acyclic graph with multiple degree zero
+        nodes creates an arborescence with multiple (weakly) connected
+        components.
+
+        """
+        G = nx.DiGraph([(0, 1), (0, 2), (1, 3), (2, 3), (5, 2)])
+        B = nx.dag_to_branching(G)
+        expected = nx.DiGraph([(0, 1), (1, 3), (0, 2), (2, 4), (5, 6), (6, 7)])
+        assert nx.is_branching(B)
+        assert not nx.is_arborescence(B)
+        assert nx.is_isomorphic(B, expected)
+
+    # # Attributes are not copied by this function. If they were, this would
+    # # be a good test to uncomment.
+    # def test_copy_attributes(self):
+    #     """Tests that node attributes are copied in the branching."""
+    #     G = nx.DiGraph([(0, 1), (0, 2), (1, 3), (2, 3)])
+    #     for v in G:
+    #         G.node[v]['label'] = str(v)
+    #     B = nx.dag_to_branching(G)
+    #     # Determine the root node of the branching.
+    #     root = next(v for v, d in B.in_degree() if d == 0)
+    #     assert_equal(B.node[root]['label'], '0')
+    #     children = B[root]
+    #     # Get the left and right children, nodes 1 and 2, respectively.
+    #     left, right = sorted(children, key=lambda v: B.node[v]['label'])
+    #     assert_equal(B.node[left]['label'], '1')
+    #     assert_equal(B.node[right]['label'], '2')
+    #     # Get the left grandchild.
+    #     children = B[left]
+    #     assert_equal(len(children), 1)
+    #     left_grandchild = arbitrary_element(children)
+    #     assert_equal(B.node[left_grandchild]['label'], '3')
+    #     # Get the right grandchild.
+    #     children = B[right]
+    #     assert_equal(len(children), 1)
+    #     right_grandchild = arbitrary_element(children)
+    #     assert_equal(B.node[right_grandchild]['label'], '3')
+
+    def test_already_arborescence(self):
+        """Tests that a directed acyclic graph that is already an
+        arborescence produces an isomorphic arborescence as output.
+
+        """
+        A = nx.balanced_tree(2, 2, create_using=nx.DiGraph())
+        B = nx.dag_to_branching(A)
+        assert nx.is_isomorphic(A, B)
+
+    def test_already_branching(self):
+        """Tests that a directed acyclic graph that is already a
+        branching produces an isomorphic branching as output.
+
+        """
+        T1 = nx.balanced_tree(2, 2, create_using=nx.DiGraph())
+        T2 = nx.balanced_tree(2, 2, create_using=nx.DiGraph())
+        G = nx.disjoint_union(T1, T2)
+        B = nx.dag_to_branching(G)
+        assert nx.is_isomorphic(G, B)
+
+    def test_not_acyclic(self):
+        """Tests that a non-acyclic graph causes an exception."""
+        with pytest.raises(nx.HasACycle):
+            G = nx.DiGraph(pairwise("abc", cyclic=True))
+            nx.dag_to_branching(G)
+
+    def test_undirected(self):
+        with pytest.raises(nx.NetworkXNotImplemented):
+            nx.dag_to_branching(nx.Graph())
+
+    def test_multigraph(self):
+        with pytest.raises(nx.NetworkXNotImplemented):
+            nx.dag_to_branching(nx.MultiGraph())
+
+    def test_multidigraph(self):
+        with pytest.raises(nx.NetworkXNotImplemented):
+            nx.dag_to_branching(nx.MultiDiGraph())
+
+
+def test_ancestors_descendants_undirected():
+    """Regression test to ensure ancestors and descendants work as expected on
+    undirected graphs."""
+    G = nx.path_graph(5)
+    nx.ancestors(G, 2) == nx.descendants(G, 2) == {0, 1, 3, 4}
+
+
+def test_compute_v_structures_raise():
+    G = nx.Graph()
+    with pytest.raises(nx.NetworkXNotImplemented, match="for undirected type"):
+        nx.compute_v_structures(G)
+
+
+def test_compute_v_structures():
+    edges = [(0, 1), (0, 2), (3, 2)]
+    G = nx.DiGraph(edges)
+
+    v_structs = set(nx.compute_v_structures(G))
+    assert len(v_structs) == 1
+    assert (0, 2, 3) in v_structs
+
+    edges = [("A", "B"), ("C", "B"), ("B", "D"), ("D", "E"), ("G", "E")]
+    G = nx.DiGraph(edges)
+    v_structs = set(nx.compute_v_structures(G))
+    assert len(v_structs) == 2
+
+
+def test_compute_v_structures_deprecated():
+    G = nx.DiGraph()
+    with pytest.deprecated_call():
+        nx.compute_v_structures(G)
+
+
+def test_v_structures_raise():
+    G = nx.Graph()
+    with pytest.raises(nx.NetworkXNotImplemented, match="for undirected type"):
+        nx.dag.v_structures(G)
+
+
+@pytest.mark.parametrize(
+    ("edgelist", "expected"),
+    (
+        (
+            [(0, 1), (0, 2), (3, 2)],
+            {(0, 2, 3)},
+        ),
+        (
+            [("A", "B"), ("C", "B"), ("D", "G"), ("D", "E"), ("G", "E")],
+            {("A", "B", "C")},
+        ),
+        ([(0, 1), (2, 1), (0, 2)], set()),  # adjacent parents case: see gh-7385
+    ),
+)
+def test_v_structures(edgelist, expected):
+    G = nx.DiGraph(edgelist)
+    v_structs = set(nx.dag.v_structures(G))
+    assert v_structs == expected
+
+
+def test_colliders_raise():
+    G = nx.Graph()
+    with pytest.raises(nx.NetworkXNotImplemented, match="for undirected type"):
+        nx.dag.colliders(G)
+
+
+@pytest.mark.parametrize(
+    ("edgelist", "expected"),
+    (
+        (
+            [(0, 1), (0, 2), (3, 2)],
+            {(0, 2, 3)},
+        ),
+        (
+            [("A", "B"), ("C", "B"), ("D", "G"), ("D", "E"), ("G", "E")],
+            {("A", "B", "C"), ("D", "E", "G")},
+        ),
+    ),
+)
+def test_colliders(edgelist, expected):
+    G = nx.DiGraph(edgelist)
+    colliders = set(nx.dag.colliders(G))
+    assert colliders == expected