"""Unit tests for the :mod:`networkx.algorithms.tree.mst` module."""
import pytest
import networkx as nx
from networkx.utils import edges_equal, nodes_equal
def test_unknown_algorithm():
with pytest.raises(ValueError):
nx.minimum_spanning_tree(nx.Graph(), algorithm="random")
with pytest.raises(
ValueError, match="random is not a valid choice for an algorithm."
):
nx.maximum_spanning_edges(nx.Graph(), algorithm="random")
class MinimumSpanningTreeTestBase:
"""Base class for test classes for minimum spanning tree algorithms.
This class contains some common tests that will be inherited by
subclasses. Each subclass must have a class attribute
:data:`algorithm` that is a string representing the algorithm to
run, as described under the ``algorithm`` keyword argument for the
:func:`networkx.minimum_spanning_edges` function. Subclasses can
then implement any algorithm-specific tests.
"""
def setup_method(self, method):
"""Creates an example graph and stores the expected minimum and
maximum spanning tree edges.
"""
# This stores the class attribute `algorithm` in an instance attribute.
self.algo = self.algorithm
# This example graph comes from Wikipedia:
# https://en.wikipedia.org/wiki/Kruskal's_algorithm
edges = [
(0, 1, 7),
(0, 3, 5),
(1, 2, 8),
(1, 3, 9),
(1, 4, 7),
(2, 4, 5),
(3, 4, 15),
(3, 5, 6),
(4, 5, 8),
(4, 6, 9),
(5, 6, 11),
]
self.G = nx.Graph()
self.G.add_weighted_edges_from(edges)
self.minimum_spanning_edgelist = [
(0, 1, {"weight": 7}),
(0, 3, {"weight": 5}),
(1, 4, {"weight": 7}),
(2, 4, {"weight": 5}),
(3, 5, {"weight": 6}),
(4, 6, {"weight": 9}),
]
self.maximum_spanning_edgelist = [
(0, 1, {"weight": 7}),
(1, 2, {"weight": 8}),
(1, 3, {"weight": 9}),
(3, 4, {"weight": 15}),
(4, 6, {"weight": 9}),
(5, 6, {"weight": 11}),
]
def test_minimum_edges(self):
edges = nx.minimum_spanning_edges(self.G, algorithm=self.algo)
# Edges from the spanning edges functions don't come in sorted
# orientation, so we need to sort each edge individually.
actual = sorted((min(u, v), max(u, v), d) for u, v, d in edges)
assert edges_equal(actual, self.minimum_spanning_edgelist)
def test_maximum_edges(self):
edges = nx.maximum_spanning_edges(self.G, algorithm=self.algo)
# Edges from the spanning edges functions don't come in sorted
# orientation, so we need to sort each edge individually.
actual = sorted((min(u, v), max(u, v), d) for u, v, d in edges)
assert edges_equal(actual, self.maximum_spanning_edgelist)
def test_without_data(self):
edges = nx.minimum_spanning_edges(self.G, algorithm=self.algo, data=False)
# Edges from the spanning edges functions don't come in sorted
# orientation, so we need to sort each edge individually.
actual = sorted((min(u, v), max(u, v)) for u, v in edges)
expected = [(u, v) for u, v, d in self.minimum_spanning_edgelist]
assert edges_equal(actual, expected)
def test_nan_weights(self):
# Edge weights NaN never appear in the spanning tree. see #2164
G = self.G
G.add_edge(0, 12, weight=float("nan"))
edges = nx.minimum_spanning_edges(
G, algorithm=self.algo, data=False, ignore_nan=True
)
actual = sorted((min(u, v), max(u, v)) for u, v in edges)
expected = [(u, v) for u, v, d in self.minimum_spanning_edgelist]
assert edges_equal(actual, expected)
# Now test for raising exception
edges = nx.minimum_spanning_edges(
G, algorithm=self.algo, data=False, ignore_nan=False
)
with pytest.raises(ValueError):
list(edges)
# test default for ignore_nan as False
edges = nx.minimum_spanning_edges(G, algorithm=self.algo, data=False)
with pytest.raises(ValueError):
list(edges)
def test_nan_weights_MultiGraph(self):
G = nx.MultiGraph()
G.add_edge(0, 12, weight=float("nan"))
edges = nx.minimum_spanning_edges(
G, algorithm="prim", data=False, ignore_nan=False
)
with pytest.raises(ValueError):
list(edges)
# test default for ignore_nan as False
edges = nx.minimum_spanning_edges(G, algorithm="prim", data=False)
with pytest.raises(ValueError):
list(edges)
def test_nan_weights_order(self):
# now try again with a nan edge at the beginning of G.nodes
edges = [
(0, 1, 7),
(0, 3, 5),
(1, 2, 8),
(1, 3, 9),
(1, 4, 7),
(2, 4, 5),
(3, 4, 15),
(3, 5, 6),
(4, 5, 8),
(4, 6, 9),
(5, 6, 11),
]
G = nx.Graph()
G.add_weighted_edges_from([(u + 1, v + 1, wt) for u, v, wt in edges])
G.add_edge(0, 7, weight=float("nan"))
edges = nx.minimum_spanning_edges(
G, algorithm=self.algo, data=False, ignore_nan=True
)
actual = sorted((min(u, v), max(u, v)) for u, v in edges)
shift = [(u + 1, v + 1) for u, v, d in self.minimum_spanning_edgelist]
assert edges_equal(actual, shift)
def test_isolated_node(self):
# now try again with an isolated node
edges = [
(0, 1, 7),
(0, 3, 5),
(1, 2, 8),
(1, 3, 9),
(1, 4, 7),
(2, 4, 5),
(3, 4, 15),
(3, 5, 6),
(4, 5, 8),
(4, 6, 9),
(5, 6, 11),
]
G = nx.Graph()
G.add_weighted_edges_from([(u + 1, v + 1, wt) for u, v, wt in edges])
G.add_node(0)
edges = nx.minimum_spanning_edges(
G, algorithm=self.algo, data=False, ignore_nan=True
)
actual = sorted((min(u, v), max(u, v)) for u, v in edges)
shift = [(u + 1, v + 1) for u, v, d in self.minimum_spanning_edgelist]
assert edges_equal(actual, shift)
def test_minimum_tree(self):
T = nx.minimum_spanning_tree(self.G, algorithm=self.algo)
actual = sorted(T.edges(data=True))
assert edges_equal(actual, self.minimum_spanning_edgelist)
def test_maximum_tree(self):
T = nx.maximum_spanning_tree(self.G, algorithm=self.algo)
actual = sorted(T.edges(data=True))
assert edges_equal(actual, self.maximum_spanning_edgelist)
def test_disconnected(self):
G = nx.Graph([(0, 1, {"weight": 1}), (2, 3, {"weight": 2})])
T = nx.minimum_spanning_tree(G, algorithm=self.algo)
assert nodes_equal(list(T), list(range(4)))
assert edges_equal(list(T.edges()), [(0, 1), (2, 3)])
def test_empty_graph(self):
G = nx.empty_graph(3)
T = nx.minimum_spanning_tree(G, algorithm=self.algo)
assert nodes_equal(sorted(T), list(range(3)))
assert T.number_of_edges() == 0
def test_attributes(self):
G = nx.Graph()
G.add_edge(1, 2, weight=1, color="red", distance=7)
G.add_edge(2, 3, weight=1, color="green", distance=2)
G.add_edge(1, 3, weight=10, color="blue", distance=1)
G.graph["foo"] = "bar"
T = nx.minimum_spanning_tree(G, algorithm=self.algo)
assert T.graph == G.graph
assert nodes_equal(T, G)
for u, v in T.edges():
assert T.adj[u][v] == G.adj[u][v]
def test_weight_attribute(self):
G = nx.Graph()
G.add_edge(0, 1, weight=1, distance=7)
G.add_edge(0, 2, weight=30, distance=1)
G.add_edge(1, 2, weight=1, distance=1)
G.add_node(3)
T = nx.minimum_spanning_tree(G, algorithm=self.algo, weight="distance")
assert nodes_equal(sorted(T), list(range(4)))
assert edges_equal(sorted(T.edges()), [(0, 2), (1, 2)])
T = nx.maximum_spanning_tree(G, algorithm=self.algo, weight="distance")
assert nodes_equal(sorted(T), list(range(4)))
assert edges_equal(sorted(T.edges()), [(0, 1), (0, 2)])
def test_minimum_spanning_edges_directed_raises(self):
DG = nx.DiGraph()
DG.add_edge(0, 1, weight=1)
with pytest.raises(nx.NetworkXNotImplemented):
list(nx.minimum_spanning_edges(DG, algorithm=self.algo))
with pytest.raises(nx.NetworkXNotImplemented):
list(nx.maximum_spanning_edges(DG, algorithm=self.algo))
class TestBoruvka(MinimumSpanningTreeTestBase):
"""Unit tests for computing a minimum (or maximum) spanning tree
using Borůvka's algorithm.
"""
algorithm = "boruvka"
def test_unicode_name(self):
"""Tests that using a Unicode string can correctly indicate
Borůvka's algorithm.
"""
edges = nx.minimum_spanning_edges(self.G, algorithm="borůvka")
# Edges from the spanning edges functions don't come in sorted
# orientation, so we need to sort each edge individually.
actual = sorted((min(u, v), max(u, v), d) for u, v, d in edges)
assert edges_equal(actual, self.minimum_spanning_edgelist)
def test_minimum_spanning_edges_multigraph_raises(self):
MG = nx.MultiGraph()
MG.add_edge(0, 1, weight=1)
with pytest.raises(nx.NetworkXNotImplemented):
list(nx.minimum_spanning_edges(MG, algorithm=self.algo))
with pytest.raises(nx.NetworkXNotImplemented):
list(nx.maximum_spanning_edges(MG, algorithm=self.algo))
class MultigraphMSTTestBase(MinimumSpanningTreeTestBase):
# Abstract class
def test_multigraph_keys_min(self):
"""Tests that the minimum spanning edges of a multigraph
preserves edge keys.
"""
G = nx.MultiGraph()
G.add_edge(0, 1, key="a", weight=2)
G.add_edge(0, 1, key="b", weight=1)
min_edges = nx.minimum_spanning_edges
mst_edges = min_edges(G, algorithm=self.algo, data=False)
assert edges_equal([(0, 1, "b")], list(mst_edges))
def test_multigraph_keys_max(self):
"""Tests that the maximum spanning edges of a multigraph
preserves edge keys.
"""
G = nx.MultiGraph()
G.add_edge(0, 1, key="a", weight=2)
G.add_edge(0, 1, key="b", weight=1)
max_edges = nx.maximum_spanning_edges
mst_edges = max_edges(G, algorithm=self.algo, data=False)
assert edges_equal([(0, 1, "a")], list(mst_edges))
class TestKruskal(MultigraphMSTTestBase):
"""Unit tests for computing a minimum (or maximum) spanning tree
using Kruskal's algorithm.
"""
algorithm = "kruskal"
def test_key_data_bool(self):
"""Tests that the keys and data values are included in
MST edges based on whether keys and data parameters are
true or false"""
G = nx.MultiGraph()
G.add_edge(1, 2, key=1, weight=2)
G.add_edge(1, 2, key=2, weight=3)
G.add_edge(3, 2, key=1, weight=2)
G.add_edge(3, 1, key=1, weight=4)
# keys are included and data is not included
mst_edges = nx.minimum_spanning_edges(
G, algorithm=self.algo, keys=True, data=False
)
assert edges_equal([(1, 2, 1), (2, 3, 1)], list(mst_edges))
# keys are not included and data is included
mst_edges = nx.minimum_spanning_edges(
G, algorithm=self.algo, keys=False, data=True
)
assert edges_equal(
[(1, 2, {"weight": 2}), (2, 3, {"weight": 2})], list(mst_edges)
)
# both keys and data are not included
mst_edges = nx.minimum_spanning_edges(
G, algorithm=self.algo, keys=False, data=False
)
assert edges_equal([(1, 2), (2, 3)], list(mst_edges))
# both keys and data are included
mst_edges = nx.minimum_spanning_edges(
G, algorithm=self.algo, keys=True, data=True
)
assert edges_equal(
[(1, 2, 1, {"weight": 2}), (2, 3, 1, {"weight": 2})], list(mst_edges)
)
class TestPrim(MultigraphMSTTestBase):
"""Unit tests for computing a minimum (or maximum) spanning tree
using Prim's algorithm.
"""
algorithm = "prim"
def test_prim_mst_edges_simple_graph(self):
H = nx.Graph()
H.add_edge(1, 2, key=2, weight=3)
H.add_edge(3, 2, key=1, weight=2)
H.add_edge(3, 1, key=1, weight=4)
mst_edges = nx.minimum_spanning_edges(H, algorithm=self.algo, ignore_nan=True)
assert edges_equal(
[(1, 2, {"key": 2, "weight": 3}), (2, 3, {"key": 1, "weight": 2})],
list(mst_edges),
)
def test_ignore_nan(self):
"""Tests that the edges with NaN weights are ignored or
raise an Error based on ignore_nan is true or false"""
H = nx.MultiGraph()
H.add_edge(1, 2, key=1, weight=float("nan"))
H.add_edge(1, 2, key=2, weight=3)
H.add_edge(3, 2, key=1, weight=2)
H.add_edge(3, 1, key=1, weight=4)
# NaN weight edges are ignored when ignore_nan=True
mst_edges = nx.minimum_spanning_edges(H, algorithm=self.algo, ignore_nan=True)
assert edges_equal(
[(1, 2, 2, {"weight": 3}), (2, 3, 1, {"weight": 2})], list(mst_edges)
)
# NaN weight edges raise Error when ignore_nan=False
with pytest.raises(ValueError):
list(nx.minimum_spanning_edges(H, algorithm=self.algo, ignore_nan=False))
def test_multigraph_keys_tree(self):
G = nx.MultiGraph()
G.add_edge(0, 1, key="a", weight=2)
G.add_edge(0, 1, key="b", weight=1)
T = nx.minimum_spanning_tree(G, algorithm=self.algo)
assert edges_equal([(0, 1, 1)], list(T.edges(data="weight")))
def test_multigraph_keys_tree_max(self):
G = nx.MultiGraph()
G.add_edge(0, 1, key="a", weight=2)
G.add_edge(0, 1, key="b", weight=1)
T = nx.maximum_spanning_tree(G, algorithm=self.algo)
assert edges_equal([(0, 1, 2)], list(T.edges(data="weight")))
class TestSpanningTreeIterator:
"""
Tests the spanning tree iterator on the example graph in the 2005 Sörensen
and Janssens paper An Algorithm to Generate all Spanning Trees of a Graph in
Order of Increasing Cost
"""
def setup_method(self):
# Original Graph
edges = [(0, 1, 5), (1, 2, 4), (1, 4, 6), (2, 3, 5), (2, 4, 7), (3, 4, 3)]
self.G = nx.Graph()
self.G.add_weighted_edges_from(edges)
# List of lists of spanning trees in increasing order
self.spanning_trees = [
# 1, MST, cost = 17
[
(0, 1, {"weight": 5}),
(1, 2, {"weight": 4}),
(2, 3, {"weight": 5}),
(3, 4, {"weight": 3}),
],
# 2, cost = 18
[
(0, 1, {"weight": 5}),
(1, 2, {"weight": 4}),
(1, 4, {"weight": 6}),
(3, 4, {"weight": 3}),
],
# 3, cost = 19
[
(0, 1, {"weight": 5}),
(1, 4, {"weight": 6}),
(2, 3, {"weight": 5}),
(3, 4, {"weight": 3}),
],
# 4, cost = 19
[
(0, 1, {"weight": 5}),
(1, 2, {"weight": 4}),
(2, 4, {"weight": 7}),
(3, 4, {"weight": 3}),
],
# 5, cost = 20
[
(0, 1, {"weight": 5}),
(1, 2, {"weight": 4}),
(1, 4, {"weight": 6}),
(2, 3, {"weight": 5}),
],
# 6, cost = 21
[
(0, 1, {"weight": 5}),
(1, 4, {"weight": 6}),
(2, 4, {"weight": 7}),
(3, 4, {"weight": 3}),
],
# 7, cost = 21
[
(0, 1, {"weight": 5}),
(1, 2, {"weight": 4}),
(2, 3, {"weight": 5}),
(2, 4, {"weight": 7}),
],
# 8, cost = 23
[
(0, 1, {"weight": 5}),
(1, 4, {"weight": 6}),
(2, 3, {"weight": 5}),
(2, 4, {"weight": 7}),
],
]
def test_minimum_spanning_tree_iterator(self):
"""
Tests that the spanning trees are correctly returned in increasing order
"""
tree_index = 0
for tree in nx.SpanningTreeIterator(self.G):
actual = sorted(tree.edges(data=True))
assert edges_equal(actual, self.spanning_trees[tree_index])
tree_index += 1
def test_maximum_spanning_tree_iterator(self):
"""
Tests that the spanning trees are correctly returned in decreasing order
"""
tree_index = 7
for tree in nx.SpanningTreeIterator(self.G, minimum=False):
actual = sorted(tree.edges(data=True))
assert edges_equal(actual, self.spanning_trees[tree_index])
tree_index -= 1
class TestSpanningTreeMultiGraphIterator:
"""
Uses the same graph as the above class but with an added edge of twice the weight.
"""
def setup_method(self):
# New graph
edges = [
(0, 1, 5),
(0, 1, 10),
(1, 2, 4),
(1, 2, 8),
(1, 4, 6),
(1, 4, 12),
(2, 3, 5),
(2, 3, 10),
(2, 4, 7),
(2, 4, 14),
(3, 4, 3),
(3, 4, 6),
]
self.G = nx.MultiGraph()
self.G.add_weighted_edges_from(edges)
# There are 128 trees. I'd rather not list all 128 here, and computing them
# on such a small graph actually doesn't take that long.
from itertools import combinations
self.spanning_trees = []
for e in combinations(self.G.edges, 4):
tree = self.G.edge_subgraph(e)
if nx.is_tree(tree):
self.spanning_trees.append(sorted(tree.edges(keys=True, data=True)))
def test_minimum_spanning_tree_iterator_multigraph(self):
"""
Tests that the spanning trees are correctly returned in increasing order
"""
tree_index = 0
last_weight = 0
for tree in nx.SpanningTreeIterator(self.G):
actual = sorted(tree.edges(keys=True, data=True))
weight = sum([e[3]["weight"] for e in actual])
assert actual in self.spanning_trees
assert weight >= last_weight
tree_index += 1
def test_maximum_spanning_tree_iterator_multigraph(self):
"""
Tests that the spanning trees are correctly returned in decreasing order
"""
tree_index = 127
# Maximum weight tree is 46
last_weight = 50
for tree in nx.SpanningTreeIterator(self.G, minimum=False):
actual = sorted(tree.edges(keys=True, data=True))
weight = sum([e[3]["weight"] for e in actual])
assert actual in self.spanning_trees
assert weight <= last_weight
tree_index -= 1
def test_random_spanning_tree_multiplicative_small():
"""
Using a fixed seed, sample one tree for repeatability.
"""
from math import exp
pytest.importorskip("scipy")
gamma = {
(0, 1): -0.6383,
(0, 2): -0.6827,
(0, 5): 0,
(1, 2): -1.0781,
(1, 4): 0,
(2, 3): 0,
(5, 3): -0.2820,
(5, 4): -0.3327,
(4, 3): -0.9927,
}
# The undirected support of gamma
G = nx.Graph()
for u, v in gamma:
G.add_edge(u, v, lambda_key=exp(gamma[(u, v)]))
solution_edges = [(2, 3), (3, 4), (0, 5), (5, 4), (4, 1)]
solution = nx.Graph()
solution.add_edges_from(solution_edges)
sampled_tree = nx.random_spanning_tree(G, "lambda_key", seed=42)
assert nx.utils.edges_equal(solution.edges, sampled_tree.edges)
@pytest.mark.slow
def test_random_spanning_tree_multiplicative_large():
"""
Sample many trees from the distribution created in the last test
"""
from math import exp
from random import Random
pytest.importorskip("numpy")
stats = pytest.importorskip("scipy.stats")
gamma = {
(0, 1): -0.6383,
(0, 2): -0.6827,
(0, 5): 0,
(1, 2): -1.0781,
(1, 4): 0,
(2, 3): 0,
(5, 3): -0.2820,
(5, 4): -0.3327,
(4, 3): -0.9927,
}
# The undirected support of gamma
G = nx.Graph()
for u, v in gamma:
G.add_edge(u, v, lambda_key=exp(gamma[(u, v)]))
# Find the multiplicative weight for each tree.
total_weight = 0
tree_expected = {}
for t in nx.SpanningTreeIterator(G):
# Find the multiplicative weight of the spanning tree
weight = 1
for u, v, d in t.edges(data="lambda_key"):
weight *= d
tree_expected[t] = weight
total_weight += weight
# Assert that every tree has an entry in the expected distribution
assert len(tree_expected) == 75
# Set the sample size and then calculate the expected number of times we
# expect to see each tree. This test uses a near minimum sample size where
# the most unlikely tree has an expected frequency of 5.15.
# (Minimum required is 5)
#
# Here we also initialize the tree_actual dict so that we know the keys
# match between the two. We will later take advantage of the fact that since
# python 3.7 dict order is guaranteed so the expected and actual data will
# have the same order.
sample_size = 1200
tree_actual = {}
for t in tree_expected:
tree_expected[t] = (tree_expected[t] / total_weight) * sample_size
tree_actual[t] = 0
# Sample the spanning trees
#
# Assert that they are actually trees and record which of the 75 trees we
# have sampled.
#
# For repeatability, we want to take advantage of the decorators in NetworkX
# to randomly sample the same sample each time. However, if we pass in a
# constant seed to sample_spanning_tree we will get the same tree each time.
# Instead, we can create our own random number generator with a fixed seed
# and pass those into sample_spanning_tree.
rng = Random(37)
for _ in range(sample_size):
sampled_tree = nx.random_spanning_tree(G, "lambda_key", seed=rng)
assert nx.is_tree(sampled_tree)
for t in tree_expected:
if nx.utils.edges_equal(t.edges, sampled_tree.edges):
tree_actual[t] += 1
break
# Conduct a Chi squared test to see if the actual distribution matches the
# expected one at an alpha = 0.05 significance level.
#
# H_0: The distribution of trees in tree_actual matches the normalized product
# of the edge weights in the tree.
#
# H_a: The distribution of trees in tree_actual follows some other
# distribution of spanning trees.
_, p = stats.chisquare(list(tree_actual.values()), list(tree_expected.values()))
# Assert that p is greater than the significance level so that we do not
# reject the null hypothesis
assert not p < 0.05
def test_random_spanning_tree_additive_small():
"""
Sample a single spanning tree from the additive method.
"""
pytest.importorskip("scipy")
edges = {
(0, 1): 1,
(0, 2): 1,
(0, 5): 3,
(1, 2): 2,
(1, 4): 3,
(2, 3): 3,
(5, 3): 4,
(5, 4): 5,
(4, 3): 4,
}
# Build the graph
G = nx.Graph()
for u, v in edges:
G.add_edge(u, v, weight=edges[(u, v)])
solution_edges = [(0, 2), (1, 2), (2, 3), (3, 4), (3, 5)]
solution = nx.Graph()
solution.add_edges_from(solution_edges)
sampled_tree = nx.random_spanning_tree(
G, weight="weight", multiplicative=False, seed=37
)
assert nx.utils.edges_equal(solution.edges, sampled_tree.edges)
@pytest.mark.slow
def test_random_spanning_tree_additive_large():
"""
Sample many spanning trees from the additive method.
"""
from random import Random
pytest.importorskip("numpy")
stats = pytest.importorskip("scipy.stats")
edges = {
(0, 1): 1,
(0, 2): 1,
(0, 5): 3,
(1, 2): 2,
(1, 4): 3,
(2, 3): 3,
(5, 3): 4,
(5, 4): 5,
(4, 3): 4,
}
# Build the graph
G = nx.Graph()
for u, v in edges:
G.add_edge(u, v, weight=edges[(u, v)])
# Find the additive weight for each tree.
total_weight = 0
tree_expected = {}
for t in nx.SpanningTreeIterator(G):
# Find the multiplicative weight of the spanning tree
weight = 0
for u, v, d in t.edges(data="weight"):
weight += d
tree_expected[t] = weight
total_weight += weight
# Assert that every tree has an entry in the expected distribution
assert len(tree_expected) == 75
# Set the sample size and then calculate the expected number of times we
# expect to see each tree. This test uses a near minimum sample size where
# the most unlikely tree has an expected frequency of 5.07.
# (Minimum required is 5)
#
# Here we also initialize the tree_actual dict so that we know the keys
# match between the two. We will later take advantage of the fact that since
# python 3.7 dict order is guaranteed so the expected and actual data will
# have the same order.
sample_size = 500
tree_actual = {}
for t in tree_expected:
tree_expected[t] = (tree_expected[t] / total_weight) * sample_size
tree_actual[t] = 0
# Sample the spanning trees
#
# Assert that they are actually trees and record which of the 75 trees we
# have sampled.
#
# For repeatability, we want to take advantage of the decorators in NetworkX
# to randomly sample the same sample each time. However, if we pass in a
# constant seed to sample_spanning_tree we will get the same tree each time.
# Instead, we can create our own random number generator with a fixed seed
# and pass those into sample_spanning_tree.
rng = Random(37)
for _ in range(sample_size):
sampled_tree = nx.random_spanning_tree(
G, "weight", multiplicative=False, seed=rng
)
assert nx.is_tree(sampled_tree)
for t in tree_expected:
if nx.utils.edges_equal(t.edges, sampled_tree.edges):
tree_actual[t] += 1
break
# Conduct a Chi squared test to see if the actual distribution matches the
# expected one at an alpha = 0.05 significance level.
#
# H_0: The distribution of trees in tree_actual matches the normalized product
# of the edge weights in the tree.
#
# H_a: The distribution of trees in tree_actual follows some other
# distribution of spanning trees.
_, p = stats.chisquare(list(tree_actual.values()), list(tree_expected.values()))
# Assert that p is greater than the significance level so that we do not
# reject the null hypothesis
assert not p < 0.05
def test_random_spanning_tree_empty_graph():
G = nx.Graph()
rst = nx.tree.random_spanning_tree(G)
assert len(rst.nodes) == 0
assert len(rst.edges) == 0
def test_random_spanning_tree_single_node_graph():
G = nx.Graph()
G.add_node(0)
rst = nx.tree.random_spanning_tree(G)
assert len(rst.nodes) == 1
assert len(rst.edges) == 0
def test_random_spanning_tree_single_node_loop():
G = nx.Graph()
G.add_node(0)
G.add_edge(0, 0)
rst = nx.tree.random_spanning_tree(G)
assert len(rst.nodes) == 1
assert len(rst.edges) == 0
class TestNumberSpanningTrees:
@classmethod
def setup_class(cls):
global np
np = pytest.importorskip("numpy")
sp = pytest.importorskip("scipy")
def test_nst_disconnected(self):
G = nx.empty_graph(2)
assert np.isclose(nx.number_of_spanning_trees(G), 0)
def test_nst_no_nodes(self):
G = nx.Graph()
with pytest.raises(nx.NetworkXPointlessConcept):
nx.number_of_spanning_trees(G)
def test_nst_weight(self):
G = nx.Graph()
G.add_edge(1, 2, weight=1)
G.add_edge(1, 3, weight=1)
G.add_edge(2, 3, weight=2)
# weights are ignored
assert np.isclose(nx.number_of_spanning_trees(G), 3)
# including weight
assert np.isclose(nx.number_of_spanning_trees(G, weight="weight"), 5)
def test_nst_negative_weight(self):
G = nx.Graph()
G.add_edge(1, 2, weight=1)
G.add_edge(1, 3, weight=-1)
G.add_edge(2, 3, weight=-2)
# weights are ignored
assert np.isclose(nx.number_of_spanning_trees(G), 3)
# including weight
assert np.isclose(nx.number_of_spanning_trees(G, weight="weight"), -1)
def test_nst_selfloop(self):
# self-loops are ignored
G = nx.complete_graph(3)
G.add_edge(1, 1)
assert np.isclose(nx.number_of_spanning_trees(G), 3)
def test_nst_multigraph(self):
G = nx.MultiGraph()
G.add_edge(1, 2)
G.add_edge(1, 2)
G.add_edge(1, 3)
G.add_edge(2, 3)
assert np.isclose(nx.number_of_spanning_trees(G), 5)
def test_nst_complete_graph(self):
# this is known as Cayley's formula
N = 5
G = nx.complete_graph(N)
assert np.isclose(nx.number_of_spanning_trees(G), N ** (N - 2))
def test_nst_path_graph(self):
G = nx.path_graph(5)
assert np.isclose(nx.number_of_spanning_trees(G), 1)
def test_nst_cycle_graph(self):
G = nx.cycle_graph(5)
assert np.isclose(nx.number_of_spanning_trees(G), 5)
def test_nst_directed_noroot(self):
G = nx.empty_graph(3, create_using=nx.MultiDiGraph)
with pytest.raises(nx.NetworkXError):
nx.number_of_spanning_trees(G)
def test_nst_directed_root_not_exist(self):
G = nx.empty_graph(3, create_using=nx.MultiDiGraph)
with pytest.raises(nx.NetworkXError):
nx.number_of_spanning_trees(G, root=42)
def test_nst_directed_not_weak_connected(self):
G = nx.DiGraph()
G.add_edge(1, 2)
G.add_edge(3, 4)
assert np.isclose(nx.number_of_spanning_trees(G, root=1), 0)
def test_nst_directed_cycle_graph(self):
G = nx.DiGraph()
G = nx.cycle_graph(7, G)
assert np.isclose(nx.number_of_spanning_trees(G, root=0), 1)
def test_nst_directed_complete_graph(self):
G = nx.DiGraph()
G = nx.complete_graph(7, G)
assert np.isclose(nx.number_of_spanning_trees(G, root=0), 7**5)
def test_nst_directed_multi(self):
G = nx.MultiDiGraph()
G = nx.cycle_graph(3, G)
G.add_edge(1, 2)
assert np.isclose(nx.number_of_spanning_trees(G, root=0), 2)
def test_nst_directed_selfloop(self):
G = nx.MultiDiGraph()
G = nx.cycle_graph(3, G)
G.add_edge(1, 1)
assert np.isclose(nx.number_of_spanning_trees(G, root=0), 1)
def test_nst_directed_weak_connected(self):
G = nx.MultiDiGraph()
G = nx.cycle_graph(3, G)
G.remove_edge(1, 2)
assert np.isclose(nx.number_of_spanning_trees(G, root=0), 0)
def test_nst_directed_weighted(self):
# from root=1:
# arborescence 1: 1->2, 1->3, weight=2*1
# arborescence 2: 1->2, 2->3, weight=2*3
G = nx.DiGraph()
G.add_edge(1, 2, weight=2)
G.add_edge(1, 3, weight=1)
G.add_edge(2, 3, weight=3)
Nst = nx.number_of_spanning_trees(G, root=1, weight="weight")
assert np.isclose(Nst, 8)
Nst = nx.number_of_spanning_trees(G, root=2, weight="weight")
assert np.isclose(Nst, 0)
Nst = nx.number_of_spanning_trees(G, root=3, weight="weight")
assert np.isclose(Nst, 0)