File: //lib/python3/dist-packages/networkx/algorithms/tree/tests/test_branchings.py
import pytest
np = pytest.importorskip('numpy')
import networkx as nx
from networkx.algorithms.tree import branchings
from networkx.algorithms.tree import recognition
from networkx.testing import *
#
# Explicitly discussed examples from Edmonds paper.
#
# Used in Figures A-F.
#
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)
# We convert to MultiDiGraph after using from_numpy_matrix
# https://github.com/networkx/networkx/pull/1305
def G1():
G = nx.DiGraph()
G = nx.from_numpy_matrix(G_array, create_using=G)
G = nx.MultiDiGraph(G)
return G
def G2():
# Now we shift all the weights by -10.
# Should not affect optimal arborescence, but does affect optimal branching.
G = nx.DiGraph()
Garr = G_array.copy()
Garr[np.nonzero(Garr)] -= 10
G = nx.from_numpy_matrix(Garr, create_using=G)
G = nx.MultiDiGraph(G)
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)
# If we have an exception, let's see the edges.
print(e1)
print(e2)
print
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_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 = [(set([0, 1]), 7), (set([0, 3]), 5), (set([3, 5]), 6),
(set([1, 4]), 7), (set([4, 2]), 5), (set([4, 6]), 9)]
assert x.number_of_edges() == len(edges)
for u, v, d in x.edges(data=True):
assert (set([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.DiGraph()
G = nx.from_numpy_matrix(-G_array, create_using=G)
# 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_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']