path: root/networkx/algorithms/tree/tests/test_branchings.py

import math
from operator import itemgetter

import pytest

np = pytest.importorskip("numpy")

import networkx as nx
from networkx.algorithms.tree import branchings, recognition

#
# Explicitly discussed examples from Edmonds paper.
#

# Used in Figures A-F.
#
# fmt: off
G_array = np.array([
    # 0   1   2   3   4   5   6   7   8
    [0, 0, 12, 0, 12, 0, 0, 0, 0],  # 0
    [4, 0, 0, 0, 0, 13, 0, 0, 0],  # 1
    [0, 17, 0, 21, 0, 12, 0, 0, 0],  # 2
    [5, 0, 0, 0, 17, 0, 18, 0, 0],  # 3
    [0, 0, 0, 0, 0, 0, 0, 12, 0],  # 4
    [0, 0, 0, 0, 0, 0, 14, 0, 12],  # 5
    [0, 0, 21, 0, 0, 0, 0, 0, 15],  # 6
    [0, 0, 0, 19, 0, 0, 15, 0, 0],  # 7
    [0, 0, 0, 0, 0, 0, 0, 18, 0],  # 8
], dtype=int)


# fmt: on


def G1():
    G = nx.from_numpy_array(G_array, create_using=nx.MultiDiGraph)
    return G


def G2():
    # Now we shift all the weights by -10.
    # Should not affect optimal arborescence, but does affect optimal branching.
    Garr = G_array.copy()
    Garr[np.nonzero(Garr)] -= 10
    G = nx.from_numpy_array(Garr, create_using=nx.MultiDiGraph)
    return G


# An optimal branching for G1 that is also a spanning arborescence. So it is
# also an optimal spanning arborescence.
#
optimal_arborescence_1 = [
    (0, 2, 12),
    (2, 1, 17),
    (2, 3, 21),
    (1, 5, 13),
    (3, 4, 17),
    (3, 6, 18),
    (6, 8, 15),
    (8, 7, 18),
]

# For G2, the optimal branching of G1 (with shifted weights) is no longer
# an optimal branching, but it is still an optimal spanning arborescence
# (just with shifted weights). An optimal branching for G2 is similar to what
# appears in figure G (this is greedy_subopt_branching_1a below), but with the
# edge (3, 0, 5), which is now (3, 0, -5), removed. Thus, the optimal branching
# is not a spanning arborescence. The code finds optimal_branching_2a.
# An alternative and equivalent branching is optimal_branching_2b. We would
# need to modify the code to iterate through all equivalent optimal branchings.
#
# These are maximal branchings or arborescences.
optimal_branching_2a = [
    (5, 6, 4),
    (6, 2, 11),
    (6, 8, 5),
    (8, 7, 8),
    (2, 1, 7),
    (2, 3, 11),
    (3, 4, 7),
]
optimal_branching_2b = [
    (8, 7, 8),
    (7, 3, 9),
    (3, 4, 7),
    (3, 6, 8),
    (6, 2, 11),
    (2, 1, 7),
    (1, 5, 3),
]
optimal_arborescence_2 = [
    (0, 2, 2),
    (2, 1, 7),
    (2, 3, 11),
    (1, 5, 3),
    (3, 4, 7),
    (3, 6, 8),
    (6, 8, 5),
    (8, 7, 8),
]

# Two suboptimal maximal branchings on G1 obtained from a greedy algorithm.
# 1a matches what is shown in Figure G in Edmonds's paper.
greedy_subopt_branching_1a = [
    (5, 6, 14),
    (6, 2, 21),
    (6, 8, 15),
    (8, 7, 18),
    (2, 1, 17),
    (2, 3, 21),
    (3, 0, 5),
    (3, 4, 17),
]
greedy_subopt_branching_1b = [
    (8, 7, 18),
    (7, 6, 15),
    (6, 2, 21),
    (2, 1, 17),
    (2, 3, 21),
    (1, 5, 13),
    (3, 0, 5),
    (3, 4, 17),
]


def build_branching(edges):
    G = nx.DiGraph()
    for u, v, weight in edges:
        G.add_edge(u, v, weight=weight)
    return G


def sorted_edges(G, attr="weight", default=1):
    edges = [(u, v, data.get(attr, default)) for (u, v, data) in G.edges(data=True)]
    edges = sorted(edges, key=lambda x: (x[2], x[1], x[0]))
    return edges


def assert_equal_branchings(G1, G2, attr="weight", default=1):
    edges1 = list(G1.edges(data=True))
    edges2 = list(G2.edges(data=True))
    assert len(edges1) == len(edges2)

    # Grab the weights only.
    e1 = sorted_edges(G1, attr, default)
    e2 = sorted_edges(G2, attr, default)

    for a, b in zip(e1, e2):
        assert a[:2] == b[:2]
        np.testing.assert_almost_equal(a[2], b[2])


################


def test_optimal_branching1():
    G = build_branching(optimal_arborescence_1)
    assert recognition.is_arborescence(G), True
    assert branchings.branching_weight(G) == 131


def test_optimal_branching2a():
    G = build_branching(optimal_branching_2a)
    assert recognition.is_arborescence(G), True
    assert branchings.branching_weight(G) == 53


def test_optimal_branching2b():
    G = build_branching(optimal_branching_2b)
    assert recognition.is_arborescence(G), True
    assert branchings.branching_weight(G) == 53


def test_optimal_arborescence2():
    G = build_branching(optimal_arborescence_2)
    assert recognition.is_arborescence(G), True
    assert branchings.branching_weight(G) == 51


def test_greedy_suboptimal_branching1a():
    G = build_branching(greedy_subopt_branching_1a)
    assert recognition.is_arborescence(G), True
    assert branchings.branching_weight(G) == 128


def test_greedy_suboptimal_branching1b():
    G = build_branching(greedy_subopt_branching_1b)
    assert recognition.is_arborescence(G), True
    assert branchings.branching_weight(G) == 127


def test_greedy_max1():
    # Standard test.
    #
    G = G1()
    B = branchings.greedy_branching(G)
    # There are only two possible greedy branchings. The sorting is such
    # that it should equal the second suboptimal branching: 1b.
    B_ = build_branching(greedy_subopt_branching_1b)
    assert_equal_branchings(B, B_)


def test_greedy_branching_kwarg_kind():
    G = G1()
    with pytest.raises(nx.NetworkXException, match="Unknown value for `kind`."):
        B = branchings.greedy_branching(G, kind="lol")


def test_greedy_branching_for_unsortable_nodes():
    G = nx.DiGraph()
    G.add_weighted_edges_from([((2, 3), 5, 1), (3, "a", 1), (2, 4, 5)])
    edges = [(u, v, data.get("weight", 1)) for (u, v, data) in G.edges(data=True)]
    with pytest.raises(TypeError):
        edges.sort(key=itemgetter(2, 0, 1), reverse=True)
    B = branchings.greedy_branching(G, kind="max").edges(data=True)
    assert list(B) == [
        ((2, 3), 5, {"weight": 1}),
        (3, "a", {"weight": 1}),
        (2, 4, {"weight": 5}),
    ]


def test_greedy_max2():
    # Different default weight.
    #
    G = G1()
    del G[1][0][0]["weight"]
    B = branchings.greedy_branching(G, default=6)
    # Chosen so that edge (3,0,5) is not selected and (1,0,6) is instead.

    edges = [
        (1, 0, 6),
        (1, 5, 13),
        (7, 6, 15),
        (2, 1, 17),
        (3, 4, 17),
        (8, 7, 18),
        (2, 3, 21),
        (6, 2, 21),
    ]
    B_ = build_branching(edges)
    assert_equal_branchings(B, B_)


def test_greedy_max3():
    # All equal weights.
    #
    G = G1()
    B = branchings.greedy_branching(G, attr=None)

    # This is mostly arbitrary...the output was generated by running the algo.
    edges = [
        (2, 1, 1),
        (3, 0, 1),
        (3, 4, 1),
        (5, 8, 1),
        (6, 2, 1),
        (7, 3, 1),
        (7, 6, 1),
        (8, 7, 1),
    ]
    B_ = build_branching(edges)
    assert_equal_branchings(B, B_, default=1)


def test_greedy_min():
    G = G1()
    B = branchings.greedy_branching(G, kind="min")

    edges = [
        (1, 0, 4),
        (0, 2, 12),
        (0, 4, 12),
        (2, 5, 12),
        (4, 7, 12),
        (5, 8, 12),
        (5, 6, 14),
        (7, 3, 19),
    ]
    B_ = build_branching(edges)
    assert_equal_branchings(B, B_)


def test_edmonds1_maxbranch():
    G = G1()
    x = branchings.maximum_branching(G)
    x_ = build_branching(optimal_arborescence_1)
    assert_equal_branchings(x, x_)


def test_edmonds1_maxarbor():
    G = G1()
    x = branchings.maximum_spanning_arborescence(G)
    x_ = build_branching(optimal_arborescence_1)
    assert_equal_branchings(x, x_)


def test_edmonds2_maxbranch():
    G = G2()
    x = branchings.maximum_branching(G)
    x_ = build_branching(optimal_branching_2a)
    assert_equal_branchings(x, x_)


def test_edmonds2_maxarbor():
    G = G2()
    x = branchings.maximum_spanning_arborescence(G)
    x_ = build_branching(optimal_arborescence_2)
    assert_equal_branchings(x, x_)


def test_edmonds2_minarbor():
    G = G1()
    x = branchings.minimum_spanning_arborescence(G)
    # This was obtained from algorithm. Need to verify it independently.
    # Branch weight is: 96
    edges = [
        (3, 0, 5),
        (0, 2, 12),
        (0, 4, 12),
        (2, 5, 12),
        (4, 7, 12),
        (5, 8, 12),
        (5, 6, 14),
        (2, 1, 17),
    ]
    x_ = build_branching(edges)
    assert_equal_branchings(x, x_)


def test_edmonds3_minbranch1():
    G = G1()
    x = branchings.minimum_branching(G)
    edges = []
    x_ = build_branching(edges)
    assert_equal_branchings(x, x_)


def test_edmonds3_minbranch2():
    G = G1()
    G.add_edge(8, 9, weight=-10)
    x = branchings.minimum_branching(G)
    edges = [(8, 9, -10)]
    x_ = build_branching(edges)
    assert_equal_branchings(x, x_)


# Need more tests


def test_mst():
    # Make sure we get the same results for undirected graphs.
    # Example from: https://en.wikipedia.org/wiki/Kruskal's_algorithm
    G = nx.Graph()
    edgelist = [
        (0, 3, [("weight", 5)]),
        (0, 1, [("weight", 7)]),
        (1, 3, [("weight", 9)]),
        (1, 2, [("weight", 8)]),
        (1, 4, [("weight", 7)]),
        (3, 4, [("weight", 15)]),
        (3, 5, [("weight", 6)]),
        (2, 4, [("weight", 5)]),
        (4, 5, [("weight", 8)]),
        (4, 6, [("weight", 9)]),
        (5, 6, [("weight", 11)]),
    ]
    G.add_edges_from(edgelist)
    G = G.to_directed()
    x = branchings.minimum_spanning_arborescence(G)

    edges = [
        ({0, 1}, 7),
        ({0, 3}, 5),
        ({3, 5}, 6),
        ({1, 4}, 7),
        ({4, 2}, 5),
        ({4, 6}, 9),
    ]

    assert x.number_of_edges() == len(edges)
    for u, v, d in x.edges(data=True):
        assert ({u, v}, d["weight"]) in edges


def test_mixed_nodetypes():
    # Smoke test to make sure no TypeError is raised for mixed node types.
    G = nx.Graph()
    edgelist = [(0, 3, [("weight", 5)]), (0, "1", [("weight", 5)])]
    G.add_edges_from(edgelist)
    G = G.to_directed()
    x = branchings.minimum_spanning_arborescence(G)


def test_edmonds1_minbranch():
    # Using -G_array and min should give the same as optimal_arborescence_1,
    # but with all edges negative.
    edges = [(u, v, -w) for (u, v, w) in optimal_arborescence_1]

    G = nx.from_numpy_array(-G_array, create_using=nx.DiGraph)

    # Quickly make sure max branching is empty.
    x = branchings.maximum_branching(G)
    x_ = build_branching([])
    assert_equal_branchings(x, x_)

    # Now test the min branching.
    x = branchings.minimum_branching(G)
    x_ = build_branching(edges)
    assert_equal_branchings(x, x_)


def test_edge_attribute_preservation_normal_graph():
    # Test that edge attributes are preserved when finding an optimum graph
    # using the Edmonds class for normal graphs.
    G = nx.Graph()

    edgelist = [
        (0, 1, [("weight", 5), ("otherattr", 1), ("otherattr2", 3)]),
        (0, 2, [("weight", 5), ("otherattr", 2), ("otherattr2", 2)]),
        (1, 2, [("weight", 6), ("otherattr", 3), ("otherattr2", 1)]),
    ]
    G.add_edges_from(edgelist)

    ed = branchings.Edmonds(G)
    B = ed.find_optimum("weight", preserve_attrs=True, seed=1)

    assert B[0][1]["otherattr"] == 1
    assert B[0][1]["otherattr2"] == 3


def test_edge_attribute_preservation_multigraph():
    # Test that edge attributes are preserved when finding an optimum graph
    # using the Edmonds class for multigraphs.
    G = nx.MultiGraph()

    edgelist = [
        (0, 1, [("weight", 5), ("otherattr", 1), ("otherattr2", 3)]),
        (0, 2, [("weight", 5), ("otherattr", 2), ("otherattr2", 2)]),
        (1, 2, [("weight", 6), ("otherattr", 3), ("otherattr2", 1)]),
    ]
    G.add_edges_from(edgelist * 2)  # Make sure we have duplicate edge paths

    ed = branchings.Edmonds(G)
    B = ed.find_optimum("weight", preserve_attrs=True)

    assert B[0][1][0]["otherattr"] == 1
    assert B[0][1][0]["otherattr2"] == 3


def test_Edmond_kind():
    G = nx.MultiGraph()

    edgelist = [
        (0, 1, [("weight", 5), ("otherattr", 1), ("otherattr2", 3)]),
        (0, 2, [("weight", 5), ("otherattr", 2), ("otherattr2", 2)]),
        (1, 2, [("weight", 6), ("otherattr", 3), ("otherattr2", 1)]),
    ]
    G.add_edges_from(edgelist * 2)  # Make sure we have duplicate edge paths
    ed = branchings.Edmonds(G)
    with pytest.raises(nx.NetworkXException, match="Unknown value for `kind`."):
        ed.find_optimum(kind="lol", preserve_attrs=True)


def test_MultiDiGraph_EdgeKey():
    # test if more than one edges has the same key
    G = branchings.MultiDiGraph_EdgeKey()
    G.add_edge(1, 2, "A")
    with pytest.raises(Exception, match="Key 'A' is already in use."):
        G.add_edge(3, 4, "A")
    # test if invalid edge key was specified
    with pytest.raises(KeyError, match="Invalid edge key 'B'"):
        G.remove_edge_with_key("B")
    # test remove_edge_with_key works
    if G.remove_edge_with_key("A"):
        assert list(G.edges(data=True)) == []
    # test that remove_edges_from doesn't work
    G.add_edge(1, 3, "A")
    with pytest.raises(NotImplementedError):
        G.remove_edges_from([(1, 3)])


def test_edge_attribute_discard():
    # Test that edge attributes are discarded if we do not specify to keep them
    G = nx.Graph()

    edgelist = [
        (0, 1, [("weight", 5), ("otherattr", 1), ("otherattr2", 3)]),
        (0, 2, [("weight", 5), ("otherattr", 2), ("otherattr2", 2)]),
        (1, 2, [("weight", 6), ("otherattr", 3), ("otherattr2", 1)]),
    ]
    G.add_edges_from(edgelist)

    ed = branchings.Edmonds(G)
    B = ed.find_optimum("weight", preserve_attrs=False)

    edge_dict = B[0][1]
    with pytest.raises(KeyError):
        _ = edge_dict["otherattr"]


def test_partition_spanning_arborescence():
    """
    Test that we can generate minimum spanning arborescences which respect the
    given partition.
    """
    G = nx.from_numpy_array(G_array, create_using=nx.DiGraph)
    G[3][0]["partition"] = nx.EdgePartition.EXCLUDED
    G[2][3]["partition"] = nx.EdgePartition.INCLUDED
    G[7][3]["partition"] = nx.EdgePartition.EXCLUDED
    G[0][2]["partition"] = nx.EdgePartition.EXCLUDED
    G[6][2]["partition"] = nx.EdgePartition.INCLUDED

    actual_edges = [
        (0, 4, 12),
        (1, 0, 4),
        (1, 5, 13),
        (2, 3, 21),
        (4, 7, 12),
        (5, 6, 14),
        (5, 8, 12),
        (6, 2, 21),
    ]

    B = branchings.minimum_spanning_arborescence(G, partition="partition")
    assert_equal_branchings(build_branching(actual_edges), B)


def test_arborescence_iterator_min():
    """
    Tests the arborescence iterator.

    A brute force method found 680 arboresecences in this graph.
    This test will not verify all of them individually, but will check two
    things

    * The iterator returns 680 arboresecences
    * The weight of the arborescences is non-strictly increasing

    for more information please visit
    https://mjschwenne.github.io/2021/06/10/implementing-the-iterators.html
    """
    G = nx.from_numpy_array(G_array, create_using=nx.DiGraph)

    arborescence_count = 0
    arborescence_weight = -math.inf
    for B in branchings.ArborescenceIterator(G):
        arborescence_count += 1
        new_arborescence_weight = B.size(weight="weight")
        assert new_arborescence_weight >= arborescence_weight
        arborescence_weight = new_arborescence_weight

    assert arborescence_count == 680


def test_arborescence_iterator_max():
    """
    Tests the arborescence iterator.

    A brute force method found 680 arboresecences in this graph.
    This test will not verify all of them individually, but will check two
    things

    * The iterator returns 680 arboresecences
    * The weight of the arborescences is non-strictly decreasing

    for more information please visit
    https://mjschwenne.github.io/2021/06/10/implementing-the-iterators.html
    """
    G = nx.from_numpy_array(G_array, create_using=nx.DiGraph)

    arborescence_count = 0
    arborescence_weight = math.inf
    for B in branchings.ArborescenceIterator(G, minimum=False):
        arborescence_count += 1
        new_arborescence_weight = B.size(weight="weight")
        assert new_arborescence_weight <= arborescence_weight
        arborescence_weight = new_arborescence_weight

    assert arborescence_count == 680


def test_arborescence_iterator_initial_partition():
    """
    Tests the arborescence iterator with three included edges and three excluded
    in the initial partition.

    A brute force method similar to the one used in the above tests found that
    there are 16 arborescences which contain the included edges and not the
    excluded edges.
    """
    G = nx.from_numpy_array(G_array, create_using=nx.DiGraph)
    included_edges = [(1, 0), (5, 6), (8, 7)]
    excluded_edges = [(0, 2), (3, 6), (1, 5)]

    arborescence_count = 0
    arborescence_weight = -math.inf
    for B in branchings.ArborescenceIterator(
        G, init_partition=(included_edges, excluded_edges)
    ):
        arborescence_count += 1
        new_arborescence_weight = B.size(weight="weight")
        assert new_arborescence_weight >= arborescence_weight
        arborescence_weight = new_arborescence_weight
        for e in included_edges:
            assert e in B.edges
        for e in excluded_edges:
            assert e not in B.edges
    assert arborescence_count == 16