two version of R2R are hereHEADmaster

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diff --git a/.venv/lib/python3.12/site-packages/networkx/algorithms/tests/test_simple_paths.py b/.venv/lib/python3.12/site-packages/networkx/algorithms/tests/test_simple_paths.py
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+import random
+
+import pytest
+
+import networkx as nx
+from networkx import convert_node_labels_to_integers as cnlti
+from networkx.algorithms.simple_paths import (
+    _bidirectional_dijkstra,
+    _bidirectional_shortest_path,
+)
+from networkx.utils import arbitrary_element, pairwise
+
+
+class TestIsSimplePath:
+    """Unit tests for the
+    :func:`networkx.algorithms.simple_paths.is_simple_path` function.
+
+    """
+
+    def test_empty_list(self):
+        """Tests that the empty list is not a valid path, since there
+        should be a one-to-one correspondence between paths as lists of
+        nodes and paths as lists of edges.
+
+        """
+        G = nx.trivial_graph()
+        assert not nx.is_simple_path(G, [])
+
+    def test_trivial_path(self):
+        """Tests that the trivial path, a path of length one, is
+        considered a simple path in a graph.
+
+        """
+        G = nx.trivial_graph()
+        assert nx.is_simple_path(G, [0])
+
+    def test_trivial_nonpath(self):
+        """Tests that a list whose sole element is an object not in the
+        graph is not considered a simple path.
+
+        """
+        G = nx.trivial_graph()
+        assert not nx.is_simple_path(G, ["not a node"])
+
+    def test_simple_path(self):
+        G = nx.path_graph(2)
+        assert nx.is_simple_path(G, [0, 1])
+
+    def test_non_simple_path(self):
+        G = nx.path_graph(2)
+        assert not nx.is_simple_path(G, [0, 1, 0])
+
+    def test_cycle(self):
+        G = nx.cycle_graph(3)
+        assert not nx.is_simple_path(G, [0, 1, 2, 0])
+
+    def test_missing_node(self):
+        G = nx.path_graph(2)
+        assert not nx.is_simple_path(G, [0, 2])
+
+    def test_missing_starting_node(self):
+        G = nx.path_graph(2)
+        assert not nx.is_simple_path(G, [2, 0])
+
+    def test_directed_path(self):
+        G = nx.DiGraph([(0, 1), (1, 2)])
+        assert nx.is_simple_path(G, [0, 1, 2])
+
+    def test_directed_non_path(self):
+        G = nx.DiGraph([(0, 1), (1, 2)])
+        assert not nx.is_simple_path(G, [2, 1, 0])
+
+    def test_directed_cycle(self):
+        G = nx.DiGraph([(0, 1), (1, 2), (2, 0)])
+        assert not nx.is_simple_path(G, [0, 1, 2, 0])
+
+    def test_multigraph(self):
+        G = nx.MultiGraph([(0, 1), (0, 1)])
+        assert nx.is_simple_path(G, [0, 1])
+
+    def test_multidigraph(self):
+        G = nx.MultiDiGraph([(0, 1), (0, 1), (1, 0), (1, 0)])
+        assert nx.is_simple_path(G, [0, 1])
+
+
+# Tests for all_simple_paths
+def test_all_simple_paths():
+    G = nx.path_graph(4)
+    paths = nx.all_simple_paths(G, 0, 3)
+    assert {tuple(p) for p in paths} == {(0, 1, 2, 3)}
+
+
+def test_all_simple_paths_with_two_targets_emits_two_paths():
+    G = nx.path_graph(4)
+    G.add_edge(2, 4)
+    paths = nx.all_simple_paths(G, 0, [3, 4])
+    assert {tuple(p) for p in paths} == {(0, 1, 2, 3), (0, 1, 2, 4)}
+
+
+def test_digraph_all_simple_paths_with_two_targets_emits_two_paths():
+    G = nx.path_graph(4, create_using=nx.DiGraph())
+    G.add_edge(2, 4)
+    paths = nx.all_simple_paths(G, 0, [3, 4])
+    assert {tuple(p) for p in paths} == {(0, 1, 2, 3), (0, 1, 2, 4)}
+
+
+def test_all_simple_paths_with_two_targets_cutoff():
+    G = nx.path_graph(4)
+    G.add_edge(2, 4)
+    paths = nx.all_simple_paths(G, 0, [3, 4], cutoff=3)
+    assert {tuple(p) for p in paths} == {(0, 1, 2, 3), (0, 1, 2, 4)}
+
+
+def test_digraph_all_simple_paths_with_two_targets_cutoff():
+    G = nx.path_graph(4, create_using=nx.DiGraph())
+    G.add_edge(2, 4)
+    paths = nx.all_simple_paths(G, 0, [3, 4], cutoff=3)
+    assert {tuple(p) for p in paths} == {(0, 1, 2, 3), (0, 1, 2, 4)}
+
+
+def test_all_simple_paths_with_two_targets_in_line_emits_two_paths():
+    G = nx.path_graph(4)
+    paths = nx.all_simple_paths(G, 0, [2, 3])
+    assert {tuple(p) for p in paths} == {(0, 1, 2), (0, 1, 2, 3)}
+
+
+def test_all_simple_paths_ignores_cycle():
+    G = nx.cycle_graph(3, create_using=nx.DiGraph())
+    G.add_edge(1, 3)
+    paths = nx.all_simple_paths(G, 0, 3)
+    assert {tuple(p) for p in paths} == {(0, 1, 3)}
+
+
+def test_all_simple_paths_with_two_targets_inside_cycle_emits_two_paths():
+    G = nx.cycle_graph(3, create_using=nx.DiGraph())
+    G.add_edge(1, 3)
+    paths = nx.all_simple_paths(G, 0, [2, 3])
+    assert {tuple(p) for p in paths} == {(0, 1, 2), (0, 1, 3)}
+
+
+def test_all_simple_paths_source_target():
+    G = nx.path_graph(4)
+    assert list(nx.all_simple_paths(G, 1, 1)) == [[1]]
+
+
+def test_all_simple_paths_cutoff():
+    G = nx.complete_graph(4)
+    paths = nx.all_simple_paths(G, 0, 1, cutoff=1)
+    assert {tuple(p) for p in paths} == {(0, 1)}
+    paths = nx.all_simple_paths(G, 0, 1, cutoff=2)
+    assert {tuple(p) for p in paths} == {(0, 1), (0, 2, 1), (0, 3, 1)}
+
+
+def test_all_simple_paths_on_non_trivial_graph():
+    """you may need to draw this graph to make sure it is reasonable"""
+    G = nx.path_graph(5, create_using=nx.DiGraph())
+    G.add_edges_from([(0, 5), (1, 5), (1, 3), (5, 4), (4, 2), (4, 3)])
+    paths = nx.all_simple_paths(G, 1, [2, 3])
+    assert {tuple(p) for p in paths} == {
+        (1, 2),
+        (1, 3, 4, 2),
+        (1, 5, 4, 2),
+        (1, 3),
+        (1, 2, 3),
+        (1, 5, 4, 3),
+        (1, 5, 4, 2, 3),
+    }
+    paths = nx.all_simple_paths(G, 1, [2, 3], cutoff=3)
+    assert {tuple(p) for p in paths} == {
+        (1, 2),
+        (1, 3, 4, 2),
+        (1, 5, 4, 2),
+        (1, 3),
+        (1, 2, 3),
+        (1, 5, 4, 3),
+    }
+    paths = nx.all_simple_paths(G, 1, [2, 3], cutoff=2)
+    assert {tuple(p) for p in paths} == {(1, 2), (1, 3), (1, 2, 3)}
+
+
+def test_all_simple_paths_multigraph():
+    G = nx.MultiGraph([(1, 2), (1, 2)])
+    assert list(nx.all_simple_paths(G, 1, 1)) == [[1]]
+    nx.add_path(G, [3, 1, 10, 2])
+    paths = list(nx.all_simple_paths(G, 1, 2))
+    assert len(paths) == 3
+    assert {tuple(p) for p in paths} == {(1, 2), (1, 2), (1, 10, 2)}
+
+
+def test_all_simple_paths_multigraph_with_cutoff():
+    G = nx.MultiGraph([(1, 2), (1, 2), (1, 10), (10, 2)])
+    paths = list(nx.all_simple_paths(G, 1, 2, cutoff=1))
+    assert len(paths) == 2
+    assert {tuple(p) for p in paths} == {(1, 2), (1, 2)}
+
+    # See GitHub issue #6732.
+    G = nx.MultiGraph([(0, 1), (0, 2)])
+    assert list(nx.all_simple_paths(G, 0, {1, 2}, cutoff=1)) == [[0, 1], [0, 2]]
+
+
+def test_all_simple_paths_directed():
+    G = nx.DiGraph()
+    nx.add_path(G, [1, 2, 3])
+    nx.add_path(G, [3, 2, 1])
+    paths = nx.all_simple_paths(G, 1, 3)
+    assert {tuple(p) for p in paths} == {(1, 2, 3)}
+
+
+def test_all_simple_paths_empty():
+    G = nx.path_graph(4)
+    paths = nx.all_simple_paths(G, 0, 3, cutoff=2)
+    assert list(paths) == []
+
+
+def test_all_simple_paths_corner_cases():
+    assert list(nx.all_simple_paths(nx.empty_graph(2), 0, 0)) == [[0]]
+    assert list(nx.all_simple_paths(nx.empty_graph(2), 0, 1)) == []
+    assert list(nx.all_simple_paths(nx.path_graph(9), 0, 8, 0)) == []
+
+
+def test_all_simple_paths_source_in_targets():
+    # See GitHub issue #6690.
+    G = nx.path_graph(3)
+    assert list(nx.all_simple_paths(G, 0, {0, 1, 2})) == [[0], [0, 1], [0, 1, 2]]
+
+
+def hamiltonian_path(G, source):
+    source = arbitrary_element(G)
+    neighbors = set(G[source]) - {source}
+    n = len(G)
+    for target in neighbors:
+        for path in nx.all_simple_paths(G, source, target):
+            if len(path) == n:
+                yield path
+
+
+def test_hamiltonian_path():
+    from itertools import permutations
+
+    G = nx.complete_graph(4)
+    paths = [list(p) for p in hamiltonian_path(G, 0)]
+    exact = [[0] + list(p) for p in permutations([1, 2, 3], 3)]
+    assert sorted(paths) == sorted(exact)
+
+
+def test_cutoff_zero():
+    G = nx.complete_graph(4)
+    paths = nx.all_simple_paths(G, 0, 3, cutoff=0)
+    assert [list(p) for p in paths] == []
+    paths = nx.all_simple_paths(nx.MultiGraph(G), 0, 3, cutoff=0)
+    assert [list(p) for p in paths] == []
+
+
+def test_source_missing():
+    with pytest.raises(nx.NodeNotFound):
+        G = nx.Graph()
+        nx.add_path(G, [1, 2, 3])
+        list(nx.all_simple_paths(nx.MultiGraph(G), 0, 3))
+
+
+def test_target_missing():
+    with pytest.raises(nx.NodeNotFound):
+        G = nx.Graph()
+        nx.add_path(G, [1, 2, 3])
+        list(nx.all_simple_paths(nx.MultiGraph(G), 1, 4))
+
+
+# Tests for all_simple_edge_paths
+def test_all_simple_edge_paths():
+    G = nx.path_graph(4)
+    paths = nx.all_simple_edge_paths(G, 0, 3)
+    assert {tuple(p) for p in paths} == {((0, 1), (1, 2), (2, 3))}
+
+
+def test_all_simple_edge_paths_empty_path():
+    G = nx.empty_graph(1)
+    assert list(nx.all_simple_edge_paths(G, 0, 0)) == [[]]
+
+
+def test_all_simple_edge_paths_with_two_targets_emits_two_paths():
+    G = nx.path_graph(4)
+    G.add_edge(2, 4)
+    paths = nx.all_simple_edge_paths(G, 0, [3, 4])
+    assert {tuple(p) for p in paths} == {
+        ((0, 1), (1, 2), (2, 3)),
+        ((0, 1), (1, 2), (2, 4)),
+    }
+
+
+def test_digraph_all_simple_edge_paths_with_two_targets_emits_two_paths():
+    G = nx.path_graph(4, create_using=nx.DiGraph())
+    G.add_edge(2, 4)
+    paths = nx.all_simple_edge_paths(G, 0, [3, 4])
+    assert {tuple(p) for p in paths} == {
+        ((0, 1), (1, 2), (2, 3)),
+        ((0, 1), (1, 2), (2, 4)),
+    }
+
+
+def test_all_simple_edge_paths_with_two_targets_cutoff():
+    G = nx.path_graph(4)
+    G.add_edge(2, 4)
+    paths = nx.all_simple_edge_paths(G, 0, [3, 4], cutoff=3)
+    assert {tuple(p) for p in paths} == {
+        ((0, 1), (1, 2), (2, 3)),
+        ((0, 1), (1, 2), (2, 4)),
+    }
+
+
+def test_digraph_all_simple_edge_paths_with_two_targets_cutoff():
+    G = nx.path_graph(4, create_using=nx.DiGraph())
+    G.add_edge(2, 4)
+    paths = nx.all_simple_edge_paths(G, 0, [3, 4], cutoff=3)
+    assert {tuple(p) for p in paths} == {
+        ((0, 1), (1, 2), (2, 3)),
+        ((0, 1), (1, 2), (2, 4)),
+    }
+
+
+def test_all_simple_edge_paths_with_two_targets_in_line_emits_two_paths():
+    G = nx.path_graph(4)
+    paths = nx.all_simple_edge_paths(G, 0, [2, 3])
+    assert {tuple(p) for p in paths} == {((0, 1), (1, 2)), ((0, 1), (1, 2), (2, 3))}
+
+
+def test_all_simple_edge_paths_ignores_cycle():
+    G = nx.cycle_graph(3, create_using=nx.DiGraph())
+    G.add_edge(1, 3)
+    paths = nx.all_simple_edge_paths(G, 0, 3)
+    assert {tuple(p) for p in paths} == {((0, 1), (1, 3))}
+
+
+def test_all_simple_edge_paths_with_two_targets_inside_cycle_emits_two_paths():
+    G = nx.cycle_graph(3, create_using=nx.DiGraph())
+    G.add_edge(1, 3)
+    paths = nx.all_simple_edge_paths(G, 0, [2, 3])
+    assert {tuple(p) for p in paths} == {((0, 1), (1, 2)), ((0, 1), (1, 3))}
+
+
+def test_all_simple_edge_paths_source_target():
+    G = nx.path_graph(4)
+    paths = nx.all_simple_edge_paths(G, 1, 1)
+    assert list(paths) == [[]]
+
+
+def test_all_simple_edge_paths_cutoff():
+    G = nx.complete_graph(4)
+    paths = nx.all_simple_edge_paths(G, 0, 1, cutoff=1)
+    assert {tuple(p) for p in paths} == {((0, 1),)}
+    paths = nx.all_simple_edge_paths(G, 0, 1, cutoff=2)
+    assert {tuple(p) for p in paths} == {((0, 1),), ((0, 2), (2, 1)), ((0, 3), (3, 1))}
+
+
+def test_all_simple_edge_paths_on_non_trivial_graph():
+    """you may need to draw this graph to make sure it is reasonable"""
+    G = nx.path_graph(5, create_using=nx.DiGraph())
+    G.add_edges_from([(0, 5), (1, 5), (1, 3), (5, 4), (4, 2), (4, 3)])
+    paths = nx.all_simple_edge_paths(G, 1, [2, 3])
+    assert {tuple(p) for p in paths} == {
+        ((1, 2),),
+        ((1, 3), (3, 4), (4, 2)),
+        ((1, 5), (5, 4), (4, 2)),
+        ((1, 3),),
+        ((1, 2), (2, 3)),
+        ((1, 5), (5, 4), (4, 3)),
+        ((1, 5), (5, 4), (4, 2), (2, 3)),
+    }
+    paths = nx.all_simple_edge_paths(G, 1, [2, 3], cutoff=3)
+    assert {tuple(p) for p in paths} == {
+        ((1, 2),),
+        ((1, 3), (3, 4), (4, 2)),
+        ((1, 5), (5, 4), (4, 2)),
+        ((1, 3),),
+        ((1, 2), (2, 3)),
+        ((1, 5), (5, 4), (4, 3)),
+    }
+    paths = nx.all_simple_edge_paths(G, 1, [2, 3], cutoff=2)
+    assert {tuple(p) for p in paths} == {((1, 2),), ((1, 3),), ((1, 2), (2, 3))}
+
+
+def test_all_simple_edge_paths_multigraph():
+    G = nx.MultiGraph([(1, 2), (1, 2)])
+    paths = nx.all_simple_edge_paths(G, 1, 1)
+    assert list(paths) == [[]]
+    nx.add_path(G, [3, 1, 10, 2])
+    paths = list(nx.all_simple_edge_paths(G, 1, 2))
+    assert len(paths) == 3
+    assert {tuple(p) for p in paths} == {
+        ((1, 2, 0),),
+        ((1, 2, 1),),
+        ((1, 10, 0), (10, 2, 0)),
+    }
+
+
+def test_all_simple_edge_paths_multigraph_with_cutoff():
+    G = nx.MultiGraph([(1, 2), (1, 2), (1, 10), (10, 2)])
+    paths = list(nx.all_simple_edge_paths(G, 1, 2, cutoff=1))
+    assert len(paths) == 2
+    assert {tuple(p) for p in paths} == {((1, 2, 0),), ((1, 2, 1),)}
+
+
+def test_all_simple_edge_paths_directed():
+    G = nx.DiGraph()
+    nx.add_path(G, [1, 2, 3])
+    nx.add_path(G, [3, 2, 1])
+    paths = nx.all_simple_edge_paths(G, 1, 3)
+    assert {tuple(p) for p in paths} == {((1, 2), (2, 3))}
+
+
+def test_all_simple_edge_paths_empty():
+    G = nx.path_graph(4)
+    paths = nx.all_simple_edge_paths(G, 0, 3, cutoff=2)
+    assert list(paths) == []
+
+
+def test_all_simple_edge_paths_corner_cases():
+    assert list(nx.all_simple_edge_paths(nx.empty_graph(2), 0, 0)) == [[]]
+    assert list(nx.all_simple_edge_paths(nx.empty_graph(2), 0, 1)) == []
+    assert list(nx.all_simple_edge_paths(nx.path_graph(9), 0, 8, 0)) == []
+
+
+def test_all_simple_edge_paths_ignores_self_loop():
+    G = nx.Graph([(0, 0), (0, 1), (1, 1), (1, 2)])
+    assert list(nx.all_simple_edge_paths(G, 0, 2)) == [[(0, 1), (1, 2)]]
+
+
+def hamiltonian_edge_path(G, source):
+    source = arbitrary_element(G)
+    neighbors = set(G[source]) - {source}
+    n = len(G)
+    for target in neighbors:
+        for path in nx.all_simple_edge_paths(G, source, target):
+            if len(path) == n - 1:
+                yield path
+
+
+def test_hamiltonian__edge_path():
+    from itertools import permutations
+
+    G = nx.complete_graph(4)
+    paths = hamiltonian_edge_path(G, 0)
+    exact = [list(pairwise([0] + list(p))) for p in permutations([1, 2, 3], 3)]
+    assert sorted(exact) == sorted(paths)
+
+
+def test_edge_cutoff_zero():
+    G = nx.complete_graph(4)
+    paths = nx.all_simple_edge_paths(G, 0, 3, cutoff=0)
+    assert [list(p) for p in paths] == []
+    paths = nx.all_simple_edge_paths(nx.MultiGraph(G), 0, 3, cutoff=0)
+    assert [list(p) for p in paths] == []
+
+
+def test_edge_source_missing():
+    with pytest.raises(nx.NodeNotFound):
+        G = nx.Graph()
+        nx.add_path(G, [1, 2, 3])
+        list(nx.all_simple_edge_paths(nx.MultiGraph(G), 0, 3))
+
+
+def test_edge_target_missing():
+    with pytest.raises(nx.NodeNotFound):
+        G = nx.Graph()
+        nx.add_path(G, [1, 2, 3])
+        list(nx.all_simple_edge_paths(nx.MultiGraph(G), 1, 4))
+
+
+# Tests for shortest_simple_paths
+def test_shortest_simple_paths():
+    G = cnlti(nx.grid_2d_graph(4, 4), first_label=1, ordering="sorted")
+    paths = nx.shortest_simple_paths(G, 1, 12)
+    assert next(paths) == [1, 2, 3, 4, 8, 12]
+    assert next(paths) == [1, 5, 6, 7, 8, 12]
+    assert [len(path) for path in nx.shortest_simple_paths(G, 1, 12)] == sorted(
+        len(path) for path in nx.all_simple_paths(G, 1, 12)
+    )
+
+
+def test_shortest_simple_paths_singleton_path():
+    G = nx.empty_graph(3)
+    assert list(nx.shortest_simple_paths(G, 0, 0)) == [[0]]
+
+
+def test_shortest_simple_paths_directed():
+    G = nx.cycle_graph(7, create_using=nx.DiGraph())
+    paths = nx.shortest_simple_paths(G, 0, 3)
+    assert list(paths) == [[0, 1, 2, 3]]
+
+
+def test_shortest_simple_paths_directed_with_weight_function():
+    def cost(u, v, x):
+        return 1
+
+    G = cnlti(nx.grid_2d_graph(4, 4), first_label=1, ordering="sorted")
+    paths = nx.shortest_simple_paths(G, 1, 12)
+    assert next(paths) == [1, 2, 3, 4, 8, 12]
+    assert next(paths) == [1, 5, 6, 7, 8, 12]
+    assert [
+        len(path) for path in nx.shortest_simple_paths(G, 1, 12, weight=cost)
+    ] == sorted(len(path) for path in nx.all_simple_paths(G, 1, 12))
+
+
+def test_shortest_simple_paths_with_weight_function():
+    def cost(u, v, x):
+        return 1
+
+    G = nx.cycle_graph(7, create_using=nx.DiGraph())
+    paths = nx.shortest_simple_paths(G, 0, 3, weight=cost)
+    assert list(paths) == [[0, 1, 2, 3]]
+
+
+def test_shortest_simple_paths_with_none_weight_function():
+    def cost(u, v, x):
+        delta = abs(u - v)
+        # ignore interior edges
+        return 1 if (delta == 1 or delta == 4) else None
+
+    G = nx.complete_graph(5)
+    paths = nx.shortest_simple_paths(G, 0, 2, weight=cost)
+    assert list(paths) == [[0, 1, 2], [0, 4, 3, 2]]
+
+
+def test_Greg_Bernstein():
+    g1 = nx.Graph()
+    g1.add_nodes_from(["N0", "N1", "N2", "N3", "N4"])
+    g1.add_edge("N4", "N1", weight=10.0, capacity=50, name="L5")
+    g1.add_edge("N4", "N0", weight=7.0, capacity=40, name="L4")
+    g1.add_edge("N0", "N1", weight=10.0, capacity=45, name="L1")
+    g1.add_edge("N3", "N0", weight=10.0, capacity=50, name="L0")
+    g1.add_edge("N2", "N3", weight=12.0, capacity=30, name="L2")
+    g1.add_edge("N1", "N2", weight=15.0, capacity=42, name="L3")
+    solution = [["N1", "N0", "N3"], ["N1", "N2", "N3"], ["N1", "N4", "N0", "N3"]]
+    result = list(nx.shortest_simple_paths(g1, "N1", "N3", weight="weight"))
+    assert result == solution
+
+
+def test_weighted_shortest_simple_path():
+    def cost_func(path):
+        return sum(G.adj[u][v]["weight"] for (u, v) in zip(path, path[1:]))
+
+    G = nx.complete_graph(5)
+    weight = {(u, v): random.randint(1, 100) for (u, v) in G.edges()}
+    nx.set_edge_attributes(G, weight, "weight")
+    cost = 0
+    for path in nx.shortest_simple_paths(G, 0, 3, weight="weight"):
+        this_cost = cost_func(path)
+        assert cost <= this_cost
+        cost = this_cost
+
+
+def test_directed_weighted_shortest_simple_path():
+    def cost_func(path):
+        return sum(G.adj[u][v]["weight"] for (u, v) in zip(path, path[1:]))
+
+    G = nx.complete_graph(5)
+    G = G.to_directed()
+    weight = {(u, v): random.randint(1, 100) for (u, v) in G.edges()}
+    nx.set_edge_attributes(G, weight, "weight")
+    cost = 0
+    for path in nx.shortest_simple_paths(G, 0, 3, weight="weight"):
+        this_cost = cost_func(path)
+        assert cost <= this_cost
+        cost = this_cost
+
+
+def test_weighted_shortest_simple_path_issue2427():
+    G = nx.Graph()
+    G.add_edge("IN", "OUT", weight=2)
+    G.add_edge("IN", "A", weight=1)
+    G.add_edge("IN", "B", weight=2)
+    G.add_edge("B", "OUT", weight=2)
+    assert list(nx.shortest_simple_paths(G, "IN", "OUT", weight="weight")) == [
+        ["IN", "OUT"],
+        ["IN", "B", "OUT"],
+    ]
+    G = nx.Graph()
+    G.add_edge("IN", "OUT", weight=10)
+    G.add_edge("IN", "A", weight=1)
+    G.add_edge("IN", "B", weight=1)
+    G.add_edge("B", "OUT", weight=1)
+    assert list(nx.shortest_simple_paths(G, "IN", "OUT", weight="weight")) == [
+        ["IN", "B", "OUT"],
+        ["IN", "OUT"],
+    ]
+
+
+def test_directed_weighted_shortest_simple_path_issue2427():
+    G = nx.DiGraph()
+    G.add_edge("IN", "OUT", weight=2)
+    G.add_edge("IN", "A", weight=1)
+    G.add_edge("IN", "B", weight=2)
+    G.add_edge("B", "OUT", weight=2)
+    assert list(nx.shortest_simple_paths(G, "IN", "OUT", weight="weight")) == [
+        ["IN", "OUT"],
+        ["IN", "B", "OUT"],
+    ]
+    G = nx.DiGraph()
+    G.add_edge("IN", "OUT", weight=10)
+    G.add_edge("IN", "A", weight=1)
+    G.add_edge("IN", "B", weight=1)
+    G.add_edge("B", "OUT", weight=1)
+    assert list(nx.shortest_simple_paths(G, "IN", "OUT", weight="weight")) == [
+        ["IN", "B", "OUT"],
+        ["IN", "OUT"],
+    ]
+
+
+def test_weight_name():
+    G = nx.cycle_graph(7)
+    nx.set_edge_attributes(G, 1, "weight")
+    nx.set_edge_attributes(G, 1, "foo")
+    G.adj[1][2]["foo"] = 7
+    paths = list(nx.shortest_simple_paths(G, 0, 3, weight="foo"))
+    solution = [[0, 6, 5, 4, 3], [0, 1, 2, 3]]
+    assert paths == solution
+
+
+def test_ssp_source_missing():
+    with pytest.raises(nx.NodeNotFound):
+        G = nx.Graph()
+        nx.add_path(G, [1, 2, 3])
+        list(nx.shortest_simple_paths(G, 0, 3))
+
+
+def test_ssp_target_missing():
+    with pytest.raises(nx.NodeNotFound):
+        G = nx.Graph()
+        nx.add_path(G, [1, 2, 3])
+        list(nx.shortest_simple_paths(G, 1, 4))
+
+
+def test_ssp_multigraph():
+    with pytest.raises(nx.NetworkXNotImplemented):
+        G = nx.MultiGraph()
+        nx.add_path(G, [1, 2, 3])
+        list(nx.shortest_simple_paths(G, 1, 4))
+
+
+def test_ssp_source_missing2():
+    with pytest.raises(nx.NetworkXNoPath):
+        G = nx.Graph()
+        nx.add_path(G, [0, 1, 2])
+        nx.add_path(G, [3, 4, 5])
+        list(nx.shortest_simple_paths(G, 0, 3))
+
+
+def test_bidirectional_shortest_path_restricted_cycle():
+    cycle = nx.cycle_graph(7)
+    length, path = _bidirectional_shortest_path(cycle, 0, 3)
+    assert path == [0, 1, 2, 3]
+    length, path = _bidirectional_shortest_path(cycle, 0, 3, ignore_nodes=[1])
+    assert path == [0, 6, 5, 4, 3]
+
+
+def test_bidirectional_shortest_path_restricted_wheel():
+    wheel = nx.wheel_graph(6)
+    length, path = _bidirectional_shortest_path(wheel, 1, 3)
+    assert path in [[1, 0, 3], [1, 2, 3]]
+    length, path = _bidirectional_shortest_path(wheel, 1, 3, ignore_nodes=[0])
+    assert path == [1, 2, 3]
+    length, path = _bidirectional_shortest_path(wheel, 1, 3, ignore_nodes=[0, 2])
+    assert path == [1, 5, 4, 3]
+    length, path = _bidirectional_shortest_path(
+        wheel, 1, 3, ignore_edges=[(1, 0), (5, 0), (2, 3)]
+    )
+    assert path in [[1, 2, 0, 3], [1, 5, 4, 3]]
+
+
+def test_bidirectional_shortest_path_restricted_directed_cycle():
+    directed_cycle = nx.cycle_graph(7, create_using=nx.DiGraph())
+    length, path = _bidirectional_shortest_path(directed_cycle, 0, 3)
+    assert path == [0, 1, 2, 3]
+    pytest.raises(
+        nx.NetworkXNoPath,
+        _bidirectional_shortest_path,
+        directed_cycle,
+        0,
+        3,
+        ignore_nodes=[1],
+    )
+    length, path = _bidirectional_shortest_path(
+        directed_cycle, 0, 3, ignore_edges=[(2, 1)]
+    )
+    assert path == [0, 1, 2, 3]
+    pytest.raises(
+        nx.NetworkXNoPath,
+        _bidirectional_shortest_path,
+        directed_cycle,
+        0,
+        3,
+        ignore_edges=[(1, 2)],
+    )
+
+
+def test_bidirectional_shortest_path_ignore():
+    G = nx.Graph()
+    nx.add_path(G, [1, 2])
+    nx.add_path(G, [1, 3])
+    nx.add_path(G, [1, 4])
+    pytest.raises(
+        nx.NetworkXNoPath, _bidirectional_shortest_path, G, 1, 2, ignore_nodes=[1]
+    )
+    pytest.raises(
+        nx.NetworkXNoPath, _bidirectional_shortest_path, G, 1, 2, ignore_nodes=[2]
+    )
+    G = nx.Graph()
+    nx.add_path(G, [1, 3])
+    nx.add_path(G, [1, 4])
+    nx.add_path(G, [3, 2])
+    pytest.raises(
+        nx.NetworkXNoPath, _bidirectional_shortest_path, G, 1, 2, ignore_nodes=[1, 2]
+    )
+
+
+def validate_path(G, s, t, soln_len, path):
+    assert path[0] == s
+    assert path[-1] == t
+    assert soln_len == sum(
+        G[u][v].get("weight", 1) for u, v in zip(path[:-1], path[1:])
+    )
+
+
+def validate_length_path(G, s, t, soln_len, length, path):
+    assert soln_len == length
+    validate_path(G, s, t, length, path)
+
+
+def test_bidirectional_dijkstra_restricted():
+    XG = nx.DiGraph()
+    XG.add_weighted_edges_from(
+        [
+            ("s", "u", 10),
+            ("s", "x", 5),
+            ("u", "v", 1),
+            ("u", "x", 2),
+            ("v", "y", 1),
+            ("x", "u", 3),
+            ("x", "v", 5),
+            ("x", "y", 2),
+            ("y", "s", 7),
+            ("y", "v", 6),
+        ]
+    )
+
+    XG3 = nx.Graph()
+    XG3.add_weighted_edges_from(
+        [[0, 1, 2], [1, 2, 12], [2, 3, 1], [3, 4, 5], [4, 5, 1], [5, 0, 10]]
+    )
+    validate_length_path(XG, "s", "v", 9, *_bidirectional_dijkstra(XG, "s", "v"))
+    validate_length_path(
+        XG, "s", "v", 10, *_bidirectional_dijkstra(XG, "s", "v", ignore_nodes=["u"])
+    )
+    validate_length_path(
+        XG,
+        "s",
+        "v",
+        11,
+        *_bidirectional_dijkstra(XG, "s", "v", ignore_edges=[("s", "x")]),
+    )
+    pytest.raises(
+        nx.NetworkXNoPath,
+        _bidirectional_dijkstra,
+        XG,
+        "s",
+        "v",
+        ignore_nodes=["u"],
+        ignore_edges=[("s", "x")],
+    )
+    validate_length_path(XG3, 0, 3, 15, *_bidirectional_dijkstra(XG3, 0, 3))
+    validate_length_path(
+        XG3, 0, 3, 16, *_bidirectional_dijkstra(XG3, 0, 3, ignore_nodes=[1])
+    )
+    validate_length_path(
+        XG3, 0, 3, 16, *_bidirectional_dijkstra(XG3, 0, 3, ignore_edges=[(2, 3)])
+    )
+    pytest.raises(
+        nx.NetworkXNoPath,
+        _bidirectional_dijkstra,
+        XG3,
+        0,
+        3,
+        ignore_nodes=[1],
+        ignore_edges=[(5, 4)],
+    )
+
+
+def test_bidirectional_dijkstra_no_path():
+    with pytest.raises(nx.NetworkXNoPath):
+        G = nx.Graph()
+        nx.add_path(G, [1, 2, 3])
+        nx.add_path(G, [4, 5, 6])
+        _bidirectional_dijkstra(G, 1, 6)
+
+
+def test_bidirectional_dijkstra_ignore():
+    G = nx.Graph()
+    nx.add_path(G, [1, 2, 10])
+    nx.add_path(G, [1, 3, 10])
+    pytest.raises(nx.NetworkXNoPath, _bidirectional_dijkstra, G, 1, 2, ignore_nodes=[1])
+    pytest.raises(nx.NetworkXNoPath, _bidirectional_dijkstra, G, 1, 2, ignore_nodes=[2])
+    pytest.raises(
+        nx.NetworkXNoPath, _bidirectional_dijkstra, G, 1, 2, ignore_nodes=[1, 2]
+    )