import pytest

import networkx as nx
from networkx.algorithms.similarity import (
    graph_edit_distance,
    optimal_edit_paths,
    optimize_graph_edit_distance,
    _n_choose_k,
)
from networkx.generators.classic import (
    circular_ladder_graph,
    cycle_graph,
    path_graph,
    wheel_graph,
)


def nmatch(n1, n2):
    return n1 == n2


def ematch(e1, e2):
    return e1 == e2


def getCanonical():
    G = nx.Graph()
    G.add_node("A", label="A")
    G.add_node("B", label="B")
    G.add_node("C", label="C")
    G.add_node("D", label="D")
    G.add_edge("A", "B", label="a-b")
    G.add_edge("B", "C", label="b-c")
    G.add_edge("B", "D", label="b-d")
    return G


class TestSimilarity:
    @classmethod
    def setup_class(cls):
        global np
        np = pytest.importorskip("numpy")
        pytest.importorskip("scipy")

    def test_graph_edit_distance_roots_and_timeout(self):
        G0 = nx.star_graph(5)
        G1 = G0.copy()
        pytest.raises(ValueError, graph_edit_distance, G0, G1, roots=[2])
        pytest.raises(ValueError, graph_edit_distance, G0, G1, roots=[2, 3, 4])
        pytest.raises(nx.NodeNotFound, graph_edit_distance, G0, G1, roots=(9, 3))
        pytest.raises(nx.NodeNotFound, graph_edit_distance, G0, G1, roots=(3, 9))
        pytest.raises(nx.NodeNotFound, graph_edit_distance, G0, G1, roots=(9, 9))
        assert graph_edit_distance(G0, G1, roots=(1, 2)) == 0
        assert graph_edit_distance(G0, G1, roots=(0, 1)) == 8
        assert graph_edit_distance(G0, G1, roots=(1, 2), timeout=5) == 0
        assert graph_edit_distance(G0, G1, roots=(0, 1), timeout=5) == 8
        assert graph_edit_distance(G0, G1, roots=(0, 1), timeout=0.0001) is None
        # test raise on 0 timeout
        pytest.raises(nx.NetworkXError, graph_edit_distance, G0, G1, timeout=0)

    def test_graph_edit_distance(self):
        G0 = nx.Graph()
        G1 = path_graph(6)
        G2 = cycle_graph(6)
        G3 = wheel_graph(7)

        assert graph_edit_distance(G0, G0) == 0
        assert graph_edit_distance(G0, G1) == 11
        assert graph_edit_distance(G1, G0) == 11
        assert graph_edit_distance(G0, G2) == 12
        assert graph_edit_distance(G2, G0) == 12
        assert graph_edit_distance(G0, G3) == 19
        assert graph_edit_distance(G3, G0) == 19

        assert graph_edit_distance(G1, G1) == 0
        assert graph_edit_distance(G1, G2) == 1
        assert graph_edit_distance(G2, G1) == 1
        assert graph_edit_distance(G1, G3) == 8
        assert graph_edit_distance(G3, G1) == 8

        assert graph_edit_distance(G2, G2) == 0
        assert graph_edit_distance(G2, G3) == 7
        assert graph_edit_distance(G3, G2) == 7

        assert graph_edit_distance(G3, G3) == 0

    def test_graph_edit_distance_node_match(self):
        G1 = cycle_graph(5)
        G2 = cycle_graph(5)
        for n, attr in G1.nodes.items():
            attr["color"] = "red" if n % 2 == 0 else "blue"
        for n, attr in G2.nodes.items():
            attr["color"] = "red" if n % 2 == 1 else "blue"
        assert graph_edit_distance(G1, G2) == 0
        assert (
            graph_edit_distance(
                G1, G2, node_match=lambda n1, n2: n1["color"] == n2["color"]
            )
            == 1
        )

    def test_graph_edit_distance_edge_match(self):
        G1 = path_graph(6)
        G2 = path_graph(6)
        for e, attr in G1.edges.items():
            attr["color"] = "red" if min(e) % 2 == 0 else "blue"
        for e, attr in G2.edges.items():
            attr["color"] = "red" if min(e) // 3 == 0 else "blue"
        assert graph_edit_distance(G1, G2) == 0
        assert (
            graph_edit_distance(
                G1, G2, edge_match=lambda e1, e2: e1["color"] == e2["color"]
            )
            == 2
        )

    def test_graph_edit_distance_node_cost(self):
        G1 = path_graph(6)
        G2 = path_graph(6)
        for n, attr in G1.nodes.items():
            attr["color"] = "red" if n % 2 == 0 else "blue"
        for n, attr in G2.nodes.items():
            attr["color"] = "red" if n % 2 == 1 else "blue"

        def node_subst_cost(uattr, vattr):
            if uattr["color"] == vattr["color"]:
                return 1
            else:
                return 10

        def node_del_cost(attr):
            if attr["color"] == "blue":
                return 20
            else:
                return 50

        def node_ins_cost(attr):
            if attr["color"] == "blue":
                return 40
            else:
                return 100

        assert (
            graph_edit_distance(
                G1,
                G2,
                node_subst_cost=node_subst_cost,
                node_del_cost=node_del_cost,
                node_ins_cost=node_ins_cost,
            )
            == 6
        )

    def test_graph_edit_distance_edge_cost(self):
        G1 = path_graph(6)
        G2 = path_graph(6)
        for e, attr in G1.edges.items():
            attr["color"] = "red" if min(e) % 2 == 0 else "blue"
        for e, attr in G2.edges.items():
            attr["color"] = "red" if min(e) // 3 == 0 else "blue"

        def edge_subst_cost(gattr, hattr):
            if gattr["color"] == hattr["color"]:
                return 0.01
            else:
                return 0.1

        def edge_del_cost(attr):
            if attr["color"] == "blue":
                return 0.2
            else:
                return 0.5

        def edge_ins_cost(attr):
            if attr["color"] == "blue":
                return 0.4
            else:
                return 1.0

        assert (
            graph_edit_distance(
                G1,
                G2,
                edge_subst_cost=edge_subst_cost,
                edge_del_cost=edge_del_cost,
                edge_ins_cost=edge_ins_cost,
            )
            == 0.23
        )

    def test_graph_edit_distance_upper_bound(self):
        G1 = circular_ladder_graph(2)
        G2 = circular_ladder_graph(6)
        assert graph_edit_distance(G1, G2, upper_bound=5) is None
        assert graph_edit_distance(G1, G2, upper_bound=24) == 22
        assert graph_edit_distance(G1, G2) == 22

    def test_optimal_edit_paths(self):
        G1 = path_graph(3)
        G2 = cycle_graph(3)
        paths, cost = optimal_edit_paths(G1, G2)
        assert cost == 1
        assert len(paths) == 6

        def canonical(vertex_path, edge_path):
            return (
                tuple(sorted(vertex_path)),
                tuple(sorted(edge_path, key=lambda x: (None in x, x))),
            )

        expected_paths = [
            (
                [(0, 0), (1, 1), (2, 2)],
                [((0, 1), (0, 1)), ((1, 2), (1, 2)), (None, (0, 2))],
            ),
            (
                [(0, 0), (1, 2), (2, 1)],
                [((0, 1), (0, 2)), ((1, 2), (1, 2)), (None, (0, 1))],
            ),
            (
                [(0, 1), (1, 0), (2, 2)],
                [((0, 1), (0, 1)), ((1, 2), (0, 2)), (None, (1, 2))],
            ),
            (
                [(0, 1), (1, 2), (2, 0)],
                [((0, 1), (1, 2)), ((1, 2), (0, 2)), (None, (0, 1))],
            ),
            (
                [(0, 2), (1, 0), (2, 1)],
                [((0, 1), (0, 2)), ((1, 2), (0, 1)), (None, (1, 2))],
            ),
            (
                [(0, 2), (1, 1), (2, 0)],
                [((0, 1), (1, 2)), ((1, 2), (0, 1)), (None, (0, 2))],
            ),
        ]
        assert {canonical(*p) for p in paths} == {canonical(*p) for p in expected_paths}

    def test_optimize_graph_edit_distance(self):
        G1 = circular_ladder_graph(2)
        G2 = circular_ladder_graph(6)
        bestcost = 1000
        for cost in optimize_graph_edit_distance(G1, G2):
            assert cost < bestcost
            bestcost = cost
        assert bestcost == 22

    # def test_graph_edit_distance_bigger(self):
    #     G1 = circular_ladder_graph(12)
    #     G2 = circular_ladder_graph(16)
    #     assert_equal(graph_edit_distance(G1, G2), 22)

    def test_selfloops(self):
        G0 = nx.Graph()
        G1 = nx.Graph()
        G1.add_edges_from((("A", "A"), ("A", "B")))
        G2 = nx.Graph()
        G2.add_edges_from((("A", "B"), ("B", "B")))
        G3 = nx.Graph()
        G3.add_edges_from((("A", "A"), ("A", "B"), ("B", "B")))

        assert graph_edit_distance(G0, G0) == 0
        assert graph_edit_distance(G0, G1) == 4
        assert graph_edit_distance(G1, G0) == 4
        assert graph_edit_distance(G0, G2) == 4
        assert graph_edit_distance(G2, G0) == 4
        assert graph_edit_distance(G0, G3) == 5
        assert graph_edit_distance(G3, G0) == 5

        assert graph_edit_distance(G1, G1) == 0
        assert graph_edit_distance(G1, G2) == 0
        assert graph_edit_distance(G2, G1) == 0
        assert graph_edit_distance(G1, G3) == 1
        assert graph_edit_distance(G3, G1) == 1

        assert graph_edit_distance(G2, G2) == 0
        assert graph_edit_distance(G2, G3) == 1
        assert graph_edit_distance(G3, G2) == 1

        assert graph_edit_distance(G3, G3) == 0

    def test_digraph(self):
        G0 = nx.DiGraph()
        G1 = nx.DiGraph()
        G1.add_edges_from((("A", "B"), ("B", "C"), ("C", "D"), ("D", "A")))
        G2 = nx.DiGraph()
        G2.add_edges_from((("A", "B"), ("B", "C"), ("C", "D"), ("A", "D")))
        G3 = nx.DiGraph()
        G3.add_edges_from((("A", "B"), ("A", "C"), ("B", "D"), ("C", "D")))

        assert graph_edit_distance(G0, G0) == 0
        assert graph_edit_distance(G0, G1) == 8
        assert graph_edit_distance(G1, G0) == 8
        assert graph_edit_distance(G0, G2) == 8
        assert graph_edit_distance(G2, G0) == 8
        assert graph_edit_distance(G0, G3) == 8
        assert graph_edit_distance(G3, G0) == 8

        assert graph_edit_distance(G1, G1) == 0
        assert graph_edit_distance(G1, G2) == 2
        assert graph_edit_distance(G2, G1) == 2
        assert graph_edit_distance(G1, G3) == 4
        assert graph_edit_distance(G3, G1) == 4

        assert graph_edit_distance(G2, G2) == 0
        assert graph_edit_distance(G2, G3) == 2
        assert graph_edit_distance(G3, G2) == 2

        assert graph_edit_distance(G3, G3) == 0

    def test_multigraph(self):
        G0 = nx.MultiGraph()
        G1 = nx.MultiGraph()
        G1.add_edges_from((("A", "B"), ("B", "C"), ("A", "C")))
        G2 = nx.MultiGraph()
        G2.add_edges_from((("A", "B"), ("B", "C"), ("B", "C"), ("A", "C")))
        G3 = nx.MultiGraph()
        G3.add_edges_from((("A", "B"), ("B", "C"), ("A", "C"), ("A", "C"), ("A", "C")))

        assert graph_edit_distance(G0, G0) == 0
        assert graph_edit_distance(G0, G1) == 6
        assert graph_edit_distance(G1, G0) == 6
        assert graph_edit_distance(G0, G2) == 7
        assert graph_edit_distance(G2, G0) == 7
        assert graph_edit_distance(G0, G3) == 8
        assert graph_edit_distance(G3, G0) == 8

        assert graph_edit_distance(G1, G1) == 0
        assert graph_edit_distance(G1, G2) == 1
        assert graph_edit_distance(G2, G1) == 1
        assert graph_edit_distance(G1, G3) == 2
        assert graph_edit_distance(G3, G1) == 2

        assert graph_edit_distance(G2, G2) == 0
        assert graph_edit_distance(G2, G3) == 1
        assert graph_edit_distance(G3, G2) == 1

        assert graph_edit_distance(G3, G3) == 0

    def test_multidigraph(self):
        G1 = nx.MultiDiGraph()
        G1.add_edges_from(
            (
                ("hardware", "kernel"),
                ("kernel", "hardware"),
                ("kernel", "userspace"),
                ("userspace", "kernel"),
            )
        )
        G2 = nx.MultiDiGraph()
        G2.add_edges_from(
            (
                ("winter", "spring"),
                ("spring", "summer"),
                ("summer", "autumn"),
                ("autumn", "winter"),
            )
        )

        assert graph_edit_distance(G1, G2) == 5
        assert graph_edit_distance(G2, G1) == 5

    # by https://github.com/jfbeaumont
    def testCopy(self):
        G = nx.Graph()
        G.add_node("A", label="A")
        G.add_node("B", label="B")
        G.add_edge("A", "B", label="a-b")
        assert (
            graph_edit_distance(G, G.copy(), node_match=nmatch, edge_match=ematch) == 0
        )

    def testSame(self):
        G1 = nx.Graph()
        G1.add_node("A", label="A")
        G1.add_node("B", label="B")
        G1.add_edge("A", "B", label="a-b")
        G2 = nx.Graph()
        G2.add_node("A", label="A")
        G2.add_node("B", label="B")
        G2.add_edge("A", "B", label="a-b")
        assert graph_edit_distance(G1, G2, node_match=nmatch, edge_match=ematch) == 0

    def testOneEdgeLabelDiff(self):
        G1 = nx.Graph()
        G1.add_node("A", label="A")
        G1.add_node("B", label="B")
        G1.add_edge("A", "B", label="a-b")
        G2 = nx.Graph()
        G2.add_node("A", label="A")
        G2.add_node("B", label="B")
        G2.add_edge("A", "B", label="bad")
        assert graph_edit_distance(G1, G2, node_match=nmatch, edge_match=ematch) == 1

    def testOneNodeLabelDiff(self):
        G1 = nx.Graph()
        G1.add_node("A", label="A")
        G1.add_node("B", label="B")
        G1.add_edge("A", "B", label="a-b")
        G2 = nx.Graph()
        G2.add_node("A", label="Z")
        G2.add_node("B", label="B")
        G2.add_edge("A", "B", label="a-b")
        assert graph_edit_distance(G1, G2, node_match=nmatch, edge_match=ematch) == 1

    def testOneExtraNode(self):
        G1 = nx.Graph()
        G1.add_node("A", label="A")
        G1.add_node("B", label="B")
        G1.add_edge("A", "B", label="a-b")
        G2 = nx.Graph()
        G2.add_node("A", label="A")
        G2.add_node("B", label="B")
        G2.add_edge("A", "B", label="a-b")
        G2.add_node("C", label="C")
        assert graph_edit_distance(G1, G2, node_match=nmatch, edge_match=ematch) == 1

    def testOneExtraEdge(self):
        G1 = nx.Graph()
        G1.add_node("A", label="A")
        G1.add_node("B", label="B")
        G1.add_node("C", label="C")
        G1.add_node("C", label="C")
        G1.add_edge("A", "B", label="a-b")
        G2 = nx.Graph()
        G2.add_node("A", label="A")
        G2.add_node("B", label="B")
        G2.add_node("C", label="C")
        G2.add_edge("A", "B", label="a-b")
        G2.add_edge("A", "C", label="a-c")
        assert graph_edit_distance(G1, G2, node_match=nmatch, edge_match=ematch) == 1

    def testOneExtraNodeAndEdge(self):
        G1 = nx.Graph()
        G1.add_node("A", label="A")
        G1.add_node("B", label="B")
        G1.add_edge("A", "B", label="a-b")
        G2 = nx.Graph()
        G2.add_node("A", label="A")
        G2.add_node("B", label="B")
        G2.add_node("C", label="C")
        G2.add_edge("A", "B", label="a-b")
        G2.add_edge("A", "C", label="a-c")
        assert graph_edit_distance(G1, G2, node_match=nmatch, edge_match=ematch) == 2

    def testGraph1(self):
        G1 = getCanonical()
        G2 = nx.Graph()
        G2.add_node("A", label="A")
        G2.add_node("B", label="B")
        G2.add_node("D", label="D")
        G2.add_node("E", label="E")
        G2.add_edge("A", "B", label="a-b")
        G2.add_edge("B", "D", label="b-d")
        G2.add_edge("D", "E", label="d-e")
        assert graph_edit_distance(G1, G2, node_match=nmatch, edge_match=ematch) == 3

    def testGraph2(self):
        G1 = getCanonical()
        G2 = nx.Graph()
        G2.add_node("A", label="A")
        G2.add_node("B", label="B")
        G2.add_node("C", label="C")
        G2.add_node("D", label="D")
        G2.add_node("E", label="E")
        G2.add_edge("A", "B", label="a-b")
        G2.add_edge("B", "C", label="b-c")
        G2.add_edge("C", "D", label="c-d")
        G2.add_edge("C", "E", label="c-e")
        assert graph_edit_distance(G1, G2, node_match=nmatch, edge_match=ematch) == 4

    def testGraph3(self):
        G1 = getCanonical()
        G2 = nx.Graph()
        G2.add_node("A", label="A")
        G2.add_node("B", label="B")
        G2.add_node("C", label="C")
        G2.add_node("D", label="D")
        G2.add_node("E", label="E")
        G2.add_node("F", label="F")
        G2.add_node("G", label="G")
        G2.add_edge("A", "C", label="a-c")
        G2.add_edge("A", "D", label="a-d")
        G2.add_edge("D", "E", label="d-e")
        G2.add_edge("D", "F", label="d-f")
        G2.add_edge("D", "G", label="d-g")
        G2.add_edge("E", "B", label="e-b")
        assert graph_edit_distance(G1, G2, node_match=nmatch, edge_match=ematch) == 12

    def testGraph4(self):
        G1 = getCanonical()
        G2 = nx.Graph()
        G2.add_node("A", label="A")
        G2.add_node("B", label="B")
        G2.add_node("C", label="C")
        G2.add_node("D", label="D")
        G2.add_edge("A", "B", label="a-b")
        G2.add_edge("B", "C", label="b-c")
        G2.add_edge("C", "D", label="c-d")
        assert graph_edit_distance(G1, G2, node_match=nmatch, edge_match=ematch) == 2

    def testGraph4_a(self):
        G1 = getCanonical()
        G2 = nx.Graph()
        G2.add_node("A", label="A")
        G2.add_node("B", label="B")
        G2.add_node("C", label="C")
        G2.add_node("D", label="D")
        G2.add_edge("A", "B", label="a-b")
        G2.add_edge("B", "C", label="b-c")
        G2.add_edge("A", "D", label="a-d")
        assert graph_edit_distance(G1, G2, node_match=nmatch, edge_match=ematch) == 2

    def testGraph4_b(self):
        G1 = getCanonical()
        G2 = nx.Graph()
        G2.add_node("A", label="A")
        G2.add_node("B", label="B")
        G2.add_node("C", label="C")
        G2.add_node("D", label="D")
        G2.add_edge("A", "B", label="a-b")
        G2.add_edge("B", "C", label="b-c")
        G2.add_edge("B", "D", label="bad")
        assert graph_edit_distance(G1, G2, node_match=nmatch, edge_match=ematch) == 1

    # note: nx.simrank_similarity_numpy not included because returns np.array
    simrank_algs = [
        nx.simrank_similarity,
        nx.similarity._simrank_similarity_python,
    ]

    @pytest.mark.parametrize("simrank_similarity", simrank_algs)
    def test_simrank_no_source_no_target(self, simrank_similarity):
        G = nx.cycle_graph(5)
        expected = {
            0: {
                0: 1,
                1: 0.3951219505902448,
                2: 0.5707317069281646,
                3: 0.5707317069281646,
                4: 0.3951219505902449,
            },
            1: {
                0: 0.3951219505902448,
                1: 1,
                2: 0.3951219505902449,
                3: 0.5707317069281646,
                4: 0.5707317069281646,
            },
            2: {
                0: 0.5707317069281646,
                1: 0.3951219505902449,
                2: 1,
                3: 0.3951219505902449,
                4: 0.5707317069281646,
            },
            3: {
                0: 0.5707317069281646,
                1: 0.5707317069281646,
                2: 0.3951219505902449,
                3: 1,
                4: 0.3951219505902449,
            },
            4: {
                0: 0.3951219505902449,
                1: 0.5707317069281646,
                2: 0.5707317069281646,
                3: 0.3951219505902449,
                4: 1,
            },
        }
        actual = simrank_similarity(G)
        for k, v in expected.items():
            assert v == pytest.approx(actual[k], abs=1e-2)

        # For a DiGraph test, use the first graph from the paper cited in
        # the docs: https://dl.acm.org/doi/pdf/10.1145/775047.775126
        G = nx.DiGraph()
        G.add_node(0, label="Univ")
        G.add_node(1, label="ProfA")
        G.add_node(2, label="ProfB")
        G.add_node(3, label="StudentA")
        G.add_node(4, label="StudentB")
        G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 4), (4, 2), (3, 0)])

        expected = {
            0: {0: 1, 1: 0.0, 2: 0.1323363991265798, 3: 0.0, 4: 0.03387811817640443},
            1: {0: 0.0, 1: 1, 2: 0.4135512472705618, 3: 0.0, 4: 0.10586911930126384},
            2: {
                0: 0.1323363991265798,
                1: 0.4135512472705618,
                2: 1,
                3: 0.04234764772050554,
                4: 0.08822426608438655,
            },
            3: {0: 0.0, 1: 0.0, 2: 0.04234764772050554, 3: 1, 4: 0.3308409978164495},
            4: {
                0: 0.03387811817640443,
                1: 0.10586911930126384,
                2: 0.08822426608438655,
                3: 0.3308409978164495,
                4: 1,
            },
        }
        # Use the importance_factor from the paper to get the same numbers.
        actual = simrank_similarity(G, importance_factor=0.8)
        for k, v in expected.items():
            assert v == pytest.approx(actual[k], abs=1e-2)

    @pytest.mark.parametrize("simrank_similarity", simrank_algs)
    def test_simrank_source_no_target(self, simrank_similarity):
        G = nx.cycle_graph(5)
        expected = {
            0: 1,
            1: 0.3951219505902448,
            2: 0.5707317069281646,
            3: 0.5707317069281646,
            4: 0.3951219505902449,
        }
        actual = simrank_similarity(G, source=0)
        assert expected == pytest.approx(actual, abs=1e-2)

        # For a DiGraph test, use the first graph from the paper cited in
        # the docs: https://dl.acm.org/doi/pdf/10.1145/775047.775126
        G = nx.DiGraph()
        G.add_node(0, label="Univ")
        G.add_node(1, label="ProfA")
        G.add_node(2, label="ProfB")
        G.add_node(3, label="StudentA")
        G.add_node(4, label="StudentB")
        G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 4), (4, 2), (3, 0)])

        expected = {0: 1, 1: 0.0, 2: 0.1323363991265798, 3: 0.0, 4: 0.03387811817640443}
        # Use the importance_factor from the paper to get the same numbers.
        actual = simrank_similarity(G, importance_factor=0.8, source=0)
        assert expected == pytest.approx(actual, abs=1e-2)

    @pytest.mark.parametrize("simrank_similarity", simrank_algs)
    def test_simrank_noninteger_nodes(self, simrank_similarity):
        G = nx.cycle_graph(5)
        G = nx.relabel_nodes(G, dict(enumerate("abcde")))
        expected = {
            "a": 1,
            "b": 0.3951219505902448,
            "c": 0.5707317069281646,
            "d": 0.5707317069281646,
            "e": 0.3951219505902449,
        }
        actual = simrank_similarity(G, source="a")
        assert expected == pytest.approx(actual, abs=1e-2)

        # For a DiGraph test, use the first graph from the paper cited in
        # the docs: https://dl.acm.org/doi/pdf/10.1145/775047.775126
        G = nx.DiGraph()
        G.add_node(0, label="Univ")
        G.add_node(1, label="ProfA")
        G.add_node(2, label="ProfB")
        G.add_node(3, label="StudentA")
        G.add_node(4, label="StudentB")
        G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 4), (4, 2), (3, 0)])
        node_labels = dict(enumerate(nx.get_node_attributes(G, "label").values()))
        G = nx.relabel_nodes(G, node_labels)

        expected = {
            "Univ": 1,
            "ProfA": 0.0,
            "ProfB": 0.1323363991265798,
            "StudentA": 0.0,
            "StudentB": 0.03387811817640443,
        }
        # Use the importance_factor from the paper to get the same numbers.
        actual = simrank_similarity(G, importance_factor=0.8, source="Univ")
        assert expected == pytest.approx(actual, abs=1e-2)

    @pytest.mark.parametrize("simrank_similarity", simrank_algs)
    def test_simrank_source_and_target(self, simrank_similarity):
        G = nx.cycle_graph(5)
        expected = 1
        actual = simrank_similarity(G, source=0, target=0)
        assert expected == pytest.approx(actual, abs=1e-2)

        # For a DiGraph test, use the first graph from the paper cited in
        # the docs: https://dl.acm.org/doi/pdf/10.1145/775047.775126
        G = nx.DiGraph()
        G.add_node(0, label="Univ")
        G.add_node(1, label="ProfA")
        G.add_node(2, label="ProfB")
        G.add_node(3, label="StudentA")
        G.add_node(4, label="StudentB")
        G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 4), (4, 2), (3, 0)])

        expected = 0.1323363991265798
        # Use the importance_factor from the paper to get the same numbers.
        # Use the pair (0,2) because (0,0) and (0,1) have trivial results.
        actual = simrank_similarity(G, importance_factor=0.8, source=0, target=2)
        assert expected == pytest.approx(actual, abs=1e-5)

    @pytest.mark.parametrize("alg", simrank_algs)
    def test_simrank_max_iterations(self, alg):
        G = nx.cycle_graph(5)
        pytest.raises(nx.ExceededMaxIterations, alg, G, max_iterations=10)

    def test_simrank_between_versions(self):
        G = nx.cycle_graph(5)
        # _python tolerance 1e-4
        expected_python_tol4 = {
            0: 1,
            1: 0.394512499239852,
            2: 0.5703550452791322,
            3: 0.5703550452791323,
            4: 0.394512499239852,
        }
        # _numpy tolerance 1e-4
        expected_numpy_tol4 = {
            0: 1.0,
            1: 0.3947180735764555,
            2: 0.570482097206368,
            3: 0.570482097206368,
            4: 0.3947180735764555,
        }
        actual = nx.simrank_similarity(G, source=0)
        assert expected_numpy_tol4 == pytest.approx(actual, abs=1e-7)
        # versions differ at 1e-4 level but equal at 1e-3
        assert expected_python_tol4 != pytest.approx(actual, abs=1e-4)
        assert expected_python_tol4 == pytest.approx(actual, abs=1e-3)

        actual = nx.similarity._simrank_similarity_python(G, source=0)
        assert expected_python_tol4 == pytest.approx(actual, abs=1e-7)
        # versions differ at 1e-4 level but equal at 1e-3
        assert expected_numpy_tol4 != pytest.approx(actual, abs=1e-4)
        assert expected_numpy_tol4 == pytest.approx(actual, abs=1e-3)

    def test_simrank_numpy_no_source_no_target(self):
        G = nx.cycle_graph(5)
        expected = np.array(
            [
                [
                    1.0,
                    0.3947180735764555,
                    0.570482097206368,
                    0.570482097206368,
                    0.3947180735764555,
                ],
                [
                    0.3947180735764555,
                    1.0,
                    0.3947180735764555,
                    0.570482097206368,
                    0.570482097206368,
                ],
                [
                    0.570482097206368,
                    0.3947180735764555,
                    1.0,
                    0.3947180735764555,
                    0.570482097206368,
                ],
                [
                    0.570482097206368,
                    0.570482097206368,
                    0.3947180735764555,
                    1.0,
                    0.3947180735764555,
                ],
                [
                    0.3947180735764555,
                    0.570482097206368,
                    0.570482097206368,
                    0.3947180735764555,
                    1.0,
                ],
            ]
        )
        actual = nx.similarity._simrank_similarity_numpy(G)
        np.testing.assert_allclose(expected, actual, atol=1e-7)

    def test_simrank_numpy_source_no_target(self):
        G = nx.cycle_graph(5)
        expected = np.array(
            [
                1.0,
                0.3947180735764555,
                0.570482097206368,
                0.570482097206368,
                0.3947180735764555,
            ]
        )
        actual = nx.similarity._simrank_similarity_numpy(G, source=0)
        np.testing.assert_allclose(expected, actual, atol=1e-7)

    def test_simrank_numpy_source_and_target(self):
        G = nx.cycle_graph(5)
        expected = 1.0
        actual = nx.similarity._simrank_similarity_numpy(G, source=0, target=0)
        np.testing.assert_allclose(expected, actual, atol=1e-7)

    def test_n_choose_k_small_k(self):
        assert _n_choose_k(10, 4) == 210

    def test_n_choose_k_big_k(self):
        assert _n_choose_k(10, 8) == 45

    def test_n_choose_k_same(self):
        assert _n_choose_k(10, 10) == 1

    def test_n_choose_k_k_bigger_than_n(self):
        assert _n_choose_k(5, 10) == 0

    def test_panther_similarity_unweighted(self):
        np.random.seed(42)

        G = nx.Graph()
        G.add_edge(0, 1)
        G.add_edge(0, 2)
        G.add_edge(0, 3)
        G.add_edge(1, 2)
        G.add_edge(2, 4)
        expected = {3: 0.5, 2: 0.5, 1: 0.5, 4: 0.125}
        sim = nx.panther_similarity(G, 0, path_length=2)
        assert sim == expected

    def test_panther_similarity_weighted(self):
        np.random.seed(42)

        G = nx.Graph()
        G.add_edge("v1", "v2", weight=5)
        G.add_edge("v1", "v3", weight=1)
        G.add_edge("v1", "v4", weight=2)
        G.add_edge("v2", "v3", weight=0.1)
        G.add_edge("v3", "v5", weight=1)
        expected = {"v3": 0.75, "v4": 0.5, "v2": 0.5, "v5": 0.25}
        sim = nx.panther_similarity(G, "v1", path_length=2)
        assert sim == expected

    def test_generate_random_paths_unweighted(self):
        np.random.seed(42)

        index_map = {}
        num_paths = 10
        path_length = 2
        G = nx.Graph()
        G.add_edge(0, 1)
        G.add_edge(0, 2)
        G.add_edge(0, 3)
        G.add_edge(1, 2)
        G.add_edge(2, 4)
        paths = nx.generate_random_paths(
            G, num_paths, path_length=path_length, index_map=index_map
        )
        expected_paths = [
            [3, 0, 3],
            [4, 2, 1],
            [2, 1, 0],
            [2, 0, 3],
            [3, 0, 1],
            [3, 0, 1],
            [4, 2, 0],
            [2, 1, 0],
            [3, 0, 2],
            [2, 1, 2],
        ]
        expected_map = {
            0: {0, 2, 3, 4, 5, 6, 7, 8},
            1: {1, 2, 4, 5, 7, 9},
            2: {1, 2, 3, 6, 7, 8, 9},
            3: {0, 3, 4, 5, 8},
            4: {1, 6},
        }

        assert expected_paths == list(paths)
        assert expected_map == index_map

    def test_generate_random_paths_weighted(self):
        np.random.seed(42)

        index_map = {}
        num_paths = 10
        path_length = 6
        G = nx.Graph()
        G.add_edge("a", "b", weight=0.6)
        G.add_edge("a", "c", weight=0.2)
        G.add_edge("c", "d", weight=0.1)
        G.add_edge("c", "e", weight=0.7)
        G.add_edge("c", "f", weight=0.9)
        G.add_edge("a", "d", weight=0.3)
        paths = nx.generate_random_paths(
            G, num_paths, path_length=path_length, index_map=index_map
        )

        expected_paths = [
            ["d", "c", "f", "c", "d", "a", "b"],
            ["e", "c", "f", "c", "f", "c", "e"],
            ["d", "a", "b", "a", "b", "a", "c"],
            ["b", "a", "d", "a", "b", "a", "b"],
            ["d", "a", "b", "a", "b", "a", "d"],
            ["d", "a", "b", "a", "b", "a", "c"],
            ["d", "a", "b", "a", "b", "a", "b"],
            ["f", "c", "f", "c", "f", "c", "e"],
            ["d", "a", "d", "a", "b", "a", "b"],
            ["e", "c", "f", "c", "e", "c", "d"],
        ]
        expected_map = {
            "d": {0, 2, 3, 4, 5, 6, 8, 9},
            "c": {0, 1, 2, 5, 7, 9},
            "f": {0, 1, 9, 7},
            "a": {0, 2, 3, 4, 5, 6, 8},
            "b": {0, 2, 3, 4, 5, 6, 8},
            "e": {1, 9, 7},
        }

        assert expected_paths == list(paths)
        assert expected_map == index_map
