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mightyscape-1.1-deprecated/extensions/networkx/algorithms/tests/test_dag.py
2020-07-30 01:16:18 +02:00

607 lines
23 KiB
Python

from itertools import combinations, permutations
import pytest
import networkx as nx
from networkx.testing.utils import assert_edges_equal
from networkx.utils import consume
from networkx.utils import pairwise
class TestDagLongestPath(object):
"""Unit tests computing the longest path in a directed acyclic graph."""
def test_empty(self):
G = nx.DiGraph()
assert nx.dag_longest_path(G) == []
def test_unweighted1(self):
edges = [(1, 2), (2, 3), (2, 4), (3, 5), (5, 6), (3, 7)]
G = nx.DiGraph(edges)
assert nx.dag_longest_path(G) == [1, 2, 3, 5, 6]
def test_unweighted2(self):
edges = [(1, 2), (2, 3), (3, 4), (4, 5), (1, 3), (1, 5), (3, 5)]
G = nx.DiGraph(edges)
assert nx.dag_longest_path(G) == [1, 2, 3, 4, 5]
def test_weighted(self):
G = nx.DiGraph()
edges = [(1, 2, -5), (2, 3, 1), (3, 4, 1), (4, 5, 0), (3, 5, 4),
(1, 6, 2)]
G.add_weighted_edges_from(edges)
assert nx.dag_longest_path(G) == [2, 3, 5]
def test_undirected_not_implemented(self):
G = nx.Graph()
pytest.raises(nx.NetworkXNotImplemented, nx.dag_longest_path, G)
def test_unorderable_nodes(self):
"""Tests that computing the longest path does not depend on
nodes being orderable.
For more information, see issue #1989.
"""
# TODO In Python 3, instances of the `object` class are
# unorderable by default, so we wouldn't need to define our own
# class here, we could just instantiate an instance of the
# `object` class. However, we still support Python 2; when
# support for Python 2 is dropped, this test can be simplified
# by replacing `Unorderable()` by `object()`.
class Unorderable(object):
def __lt__(self, other):
error_msg = "< not supported between instances of {} and {}"
types = (type(self).__name__, type(other).__name__)
raise TypeError(error_msg.format(types))
# Create the directed path graph on four nodes in a diamond shape,
# with nodes represented as (unorderable) Python objects.
nodes = [Unorderable() for n in range(4)]
G = nx.DiGraph()
G.add_edge(nodes[0], nodes[1])
G.add_edge(nodes[0], nodes[2])
G.add_edge(nodes[2], nodes[3])
G.add_edge(nodes[1], nodes[3])
# this will raise NotImplementedError when nodes need to be ordered
nx.dag_longest_path(G)
class TestDagLongestPathLength(object):
"""Unit tests for computing the length of a longest path in a
directed acyclic graph.
"""
def test_unweighted(self):
edges = [(1, 2), (2, 3), (2, 4), (3, 5), (5, 6), (5, 7)]
G = nx.DiGraph(edges)
assert nx.dag_longest_path_length(G) == 4
edges = [(1, 2), (2, 3), (3, 4), (4, 5), (1, 3), (1, 5), (3, 5)]
G = nx.DiGraph(edges)
assert nx.dag_longest_path_length(G) == 4
# test degenerate graphs
G = nx.DiGraph()
G.add_node(1)
assert nx.dag_longest_path_length(G) == 0
def test_undirected_not_implemented(self):
G = nx.Graph()
pytest.raises(nx.NetworkXNotImplemented, nx.dag_longest_path_length, G)
def test_weighted(self):
edges = [(1, 2, -5), (2, 3, 1), (3, 4, 1), (4, 5, 0), (3, 5, 4),
(1, 6, 2)]
G = nx.DiGraph()
G.add_weighted_edges_from(edges)
assert nx.dag_longest_path_length(G) == 5
class TestDAG:
@classmethod
def setup_class(cls):
pass
def test_topological_sort1(self):
DG = nx.DiGraph([(1, 2), (1, 3), (2, 3)])
for algorithm in [nx.topological_sort,
nx.lexicographical_topological_sort]:
assert tuple(algorithm(DG)) == (1, 2, 3)
DG.add_edge(3, 2)
for algorithm in [nx.topological_sort,
nx.lexicographical_topological_sort]:
pytest.raises(nx.NetworkXUnfeasible, consume, algorithm(DG))
DG.remove_edge(2, 3)
for algorithm in [nx.topological_sort,
nx.lexicographical_topological_sort]:
assert tuple(algorithm(DG)) == (1, 3, 2)
DG.remove_edge(3, 2)
assert tuple(nx.topological_sort(DG)) in {(1, 2, 3), (1, 3, 2)}
assert tuple(nx.lexicographical_topological_sort(DG)) == (1, 2, 3)
def test_is_directed_acyclic_graph(self):
G = nx.generators.complete_graph(2)
assert not nx.is_directed_acyclic_graph(G)
assert not nx.is_directed_acyclic_graph(G.to_directed())
assert not nx.is_directed_acyclic_graph(nx.Graph([(3, 4), (4, 5)]))
assert nx.is_directed_acyclic_graph(nx.DiGraph([(3, 4), (4, 5)]))
def test_topological_sort2(self):
DG = nx.DiGraph({1: [2], 2: [3], 3: [4],
4: [5], 5: [1], 11: [12],
12: [13], 13: [14], 14: [15]})
pytest.raises(nx.NetworkXUnfeasible, consume, nx.topological_sort(DG))
assert not nx.is_directed_acyclic_graph(DG)
DG.remove_edge(1, 2)
consume(nx.topological_sort(DG))
assert nx.is_directed_acyclic_graph(DG)
def test_topological_sort3(self):
DG = nx.DiGraph()
DG.add_edges_from([(1, i) for i in range(2, 5)])
DG.add_edges_from([(2, i) for i in range(5, 9)])
DG.add_edges_from([(6, i) for i in range(9, 12)])
DG.add_edges_from([(4, i) for i in range(12, 15)])
def validate(order):
assert isinstance(order, list)
assert set(order) == set(DG)
for u, v in combinations(order, 2):
assert not nx.has_path(DG, v, u)
validate(list(nx.topological_sort(DG)))
DG.add_edge(14, 1)
pytest.raises(nx.NetworkXUnfeasible, consume, nx.topological_sort(DG))
def test_topological_sort4(self):
G = nx.Graph()
G.add_edge(1, 2)
# Only directed graphs can be topologically sorted.
pytest.raises(nx.NetworkXError, consume, nx.topological_sort(G))
def test_topological_sort5(self):
G = nx.DiGraph()
G.add_edge(0, 1)
assert list(nx.topological_sort(G)) == [0, 1]
def test_topological_sort6(self):
for algorithm in [nx.topological_sort,
nx.lexicographical_topological_sort]:
def runtime_error():
DG = nx.DiGraph([(1, 2), (2, 3), (3, 4)])
first = True
for x in algorithm(DG):
if first:
first = False
DG.add_edge(5 - x, 5)
def unfeasible_error():
DG = nx.DiGraph([(1, 2), (2, 3), (3, 4)])
first = True
for x in algorithm(DG):
if first:
first = False
DG.remove_node(4)
def runtime_error2():
DG = nx.DiGraph([(1, 2), (2, 3), (3, 4)])
first = True
for x in algorithm(DG):
if first:
first = False
DG.remove_node(2)
pytest.raises(RuntimeError, runtime_error)
pytest.raises(RuntimeError, runtime_error2)
pytest.raises(nx.NetworkXUnfeasible, unfeasible_error)
def test_all_topological_sorts_1(self):
DG = nx.DiGraph([(1, 2), (2, 3), (3, 4), (4, 5)])
assert list(nx.all_topological_sorts(DG)) == [[1, 2, 3, 4, 5]]
def test_all_topological_sorts_2(self):
DG = nx.DiGraph([(1, 3), (2, 1), (2, 4), (4, 3), (4, 5)])
assert (sorted(nx.all_topological_sorts(DG)) ==
[[2, 1, 4, 3, 5],
[2, 1, 4, 5, 3],
[2, 4, 1, 3, 5],
[2, 4, 1, 5, 3],
[2, 4, 5, 1, 3]])
def test_all_topological_sorts_3(self):
def unfeasible():
DG = nx.DiGraph([(1, 2), (2, 3), (3, 4), (4, 2), (4, 5)])
# convert to list to execute generator
list(nx.all_topological_sorts(DG))
def not_implemented():
G = nx.Graph([(1, 2), (2, 3)])
# convert to list to execute generator
list(nx.all_topological_sorts(G))
def not_implemted_2():
G = nx.MultiGraph([(1, 2), (1, 2), (2, 3)])
list(nx.all_topological_sorts(G))
pytest.raises(nx.NetworkXUnfeasible, unfeasible)
pytest.raises(nx.NetworkXNotImplemented, not_implemented)
pytest.raises(nx.NetworkXNotImplemented, not_implemted_2)
def test_all_topological_sorts_4(self):
DG = nx.DiGraph()
for i in range(7):
DG.add_node(i)
assert (sorted(map(list, permutations(DG.nodes))) ==
sorted(nx.all_topological_sorts(DG)))
def test_all_topological_sorts_multigraph_1(self):
DG = nx.MultiDiGraph([(1, 2), (1, 2), (2, 3),
(3, 4), (3, 5), (3, 5), (3, 5)])
assert (sorted(nx.all_topological_sorts(DG)) ==
sorted([[1, 2, 3, 4, 5],
[1, 2, 3, 5, 4]]))
def test_all_topological_sorts_multigraph_2(self):
N = 9
edges = []
for i in range(1, N):
edges.extend([(i, i+1)] * i)
DG = nx.MultiDiGraph(edges)
assert (list(nx.all_topological_sorts(DG)) ==
[list(range(1, N+1))])
def test_ancestors(self):
G = nx.DiGraph()
ancestors = nx.algorithms.dag.ancestors
G.add_edges_from([
(1, 2), (1, 3), (4, 2), (4, 3), (4, 5), (2, 6), (5, 6)])
assert ancestors(G, 6) == set([1, 2, 4, 5])
assert ancestors(G, 3) == set([1, 4])
assert ancestors(G, 1) == set()
pytest.raises(nx.NetworkXError, ancestors, G, 8)
def test_descendants(self):
G = nx.DiGraph()
descendants = nx.algorithms.dag.descendants
G.add_edges_from([
(1, 2), (1, 3), (4, 2), (4, 3), (4, 5), (2, 6), (5, 6)])
assert descendants(G, 1) == set([2, 3, 6])
assert descendants(G, 4) == set([2, 3, 5, 6])
assert descendants(G, 3) == set()
pytest.raises(nx.NetworkXError, descendants, G, 8)
def test_transitive_closure(self):
G = nx.DiGraph([(1, 2), (2, 3), (3, 4)])
solution = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
assert_edges_equal(nx.transitive_closure(G).edges(), solution)
G = nx.DiGraph([(1, 2), (2, 3), (2, 4)])
solution = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4)]
assert_edges_equal(nx.transitive_closure(G).edges(), solution)
G = nx.DiGraph([(1, 2), (2, 3), (3, 1)])
solution = [(1, 2), (2, 1), (2, 3), (3, 2), (1, 3), (3, 1)]
soln = sorted(solution + [(n, n) for n in G])
assert_edges_equal(sorted(nx.transitive_closure(G).edges()), soln)
G = nx.Graph([(1, 2), (2, 3), (3, 4)])
pytest.raises(nx.NetworkXNotImplemented, nx.transitive_closure, G)
# test if edge data is copied
G = nx.DiGraph([(1, 2, {"a": 3}), (2, 3, {"b": 0}), (3, 4)])
H = nx.transitive_closure(G)
for u, v in G.edges():
assert G.get_edge_data(u, v) == H.get_edge_data(u, v)
k = 10
G = nx.DiGraph((i, i + 1, {"f": "b", "weight": i}) for i in range(k))
H = nx.transitive_closure(G)
for u, v in G.edges():
assert G.get_edge_data(u, v) == H.get_edge_data(u, v)
def test_reflexive_transitive_closure(self):
G = nx.DiGraph([(1, 2), (2, 3), (3, 4)])
solution = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
soln = sorted(solution + [(n, n) for n in G])
assert_edges_equal(nx.transitive_closure(G).edges(), solution)
assert_edges_equal(nx.transitive_closure(G, False).edges(), solution)
assert_edges_equal(nx.transitive_closure(G, True).edges(), soln)
assert_edges_equal(nx.transitive_closure(G, None).edges(), solution)
G = nx.DiGraph([(1, 2), (2, 3), (2, 4)])
solution = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4)]
soln = sorted(solution + [(n, n) for n in G])
assert_edges_equal(nx.transitive_closure(G).edges(), solution)
assert_edges_equal(nx.transitive_closure(G, False).edges(), solution)
assert_edges_equal(nx.transitive_closure(G, True).edges(), soln)
assert_edges_equal(nx.transitive_closure(G, None).edges(), solution)
G = nx.DiGraph([(1, 2), (2, 3), (3, 1)])
solution = sorted([(1, 2), (2, 1), (2, 3), (3, 2), (1, 3), (3, 1)])
soln = sorted(solution + [(n, n) for n in G])
assert_edges_equal(sorted(nx.transitive_closure(G).edges()), soln)
assert_edges_equal(sorted(nx.transitive_closure(G, False).edges()), soln)
assert_edges_equal(sorted(nx.transitive_closure(G, None).edges()), solution)
assert_edges_equal(sorted(nx.transitive_closure(G, True).edges()), soln)
def test_transitive_closure_dag(self):
G = nx.DiGraph([(1, 2), (2, 3), (3, 4)])
transitive_closure = nx.algorithms.dag.transitive_closure_dag
solution = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]
assert_edges_equal(transitive_closure(G).edges(), solution)
G = nx.DiGraph([(1, 2), (2, 3), (2, 4)])
solution = [(1, 2), (1, 3), (1, 4), (2, 3), (2, 4)]
assert_edges_equal(transitive_closure(G).edges(), solution)
G = nx.Graph([(1, 2), (2, 3), (3, 4)])
pytest.raises(nx.NetworkXNotImplemented, transitive_closure, G)
# test if edge data is copied
G = nx.DiGraph([(1, 2, {"a": 3}), (2, 3, {"b": 0}), (3, 4)])
H = transitive_closure(G)
for u, v in G.edges():
assert G.get_edge_data(u, v) == H.get_edge_data(u, v)
k = 10
G = nx.DiGraph((i, i + 1, {"foo": "bar", "weight": i}) for i in range(k))
H = transitive_closure(G)
for u, v in G.edges():
assert G.get_edge_data(u, v) == H.get_edge_data(u, v)
def test_transitive_reduction(self):
G = nx.DiGraph([(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)])
transitive_reduction = nx.algorithms.dag.transitive_reduction
solution = [(1, 2), (2, 3), (3, 4)]
assert_edges_equal(transitive_reduction(G).edges(), solution)
G = nx.DiGraph([(1, 2), (1, 3), (1, 4), (2, 3), (2, 4)])
transitive_reduction = nx.algorithms.dag.transitive_reduction
solution = [(1, 2), (2, 3), (2, 4)]
assert_edges_equal(transitive_reduction(G).edges(), solution)
G = nx.Graph([(1, 2), (2, 3), (3, 4)])
pytest.raises(nx.NetworkXNotImplemented, transitive_reduction, G)
def _check_antichains(self, solution, result):
sol = [frozenset(a) for a in solution]
res = [frozenset(a) for a in result]
assert set(sol) == set(res)
def test_antichains(self):
antichains = nx.algorithms.dag.antichains
G = nx.DiGraph([(1, 2), (2, 3), (3, 4)])
solution = [[], [4], [3], [2], [1]]
self._check_antichains(list(antichains(G)), solution)
G = nx.DiGraph([(1, 2), (2, 3), (2, 4), (3, 5), (5, 6), (5, 7)])
solution = [[], [4], [7], [7, 4], [6], [6, 4], [6, 7], [6, 7, 4],
[5], [5, 4], [3], [3, 4], [2], [1]]
self._check_antichains(list(antichains(G)), solution)
G = nx.DiGraph([(1, 2), (1, 3), (3, 4), (3, 5), (5, 6)])
solution = [[], [6], [5], [4], [4, 6], [4, 5], [3], [2], [2, 6],
[2, 5], [2, 4], [2, 4, 6], [2, 4, 5], [2, 3], [1]]
self._check_antichains(list(antichains(G)), solution)
G = nx.DiGraph({0: [1, 2], 1: [4], 2: [3], 3: [4]})
solution = [[], [4], [3], [2], [1], [1, 3], [1, 2], [0]]
self._check_antichains(list(antichains(G)), solution)
G = nx.DiGraph()
self._check_antichains(list(antichains(G)), [[]])
G = nx.DiGraph()
G.add_nodes_from([0, 1, 2])
solution = [[], [0], [1], [1, 0], [2], [2, 0], [2, 1], [2, 1, 0]]
self._check_antichains(list(antichains(G)), solution)
def f(x): return list(antichains(x))
G = nx.Graph([(1, 2), (2, 3), (3, 4)])
pytest.raises(nx.NetworkXNotImplemented, f, G)
G = nx.DiGraph([(1, 2), (2, 3), (3, 1)])
pytest.raises(nx.NetworkXUnfeasible, f, G)
def test_lexicographical_topological_sort(self):
G = nx.DiGraph([(1, 2), (2, 3), (1, 4), (1, 5), (2, 6)])
assert (list(nx.lexicographical_topological_sort(G)) ==
[1, 2, 3, 4, 5, 6])
assert (list(nx.lexicographical_topological_sort(
G, key=lambda x: x)) ==
[1, 2, 3, 4, 5, 6])
assert (list(nx.lexicographical_topological_sort(
G, key=lambda x: -x)) ==
[1, 5, 4, 2, 6, 3])
def test_lexicographical_topological_sort2(self):
'''
Check the case of two or more nodes with same key value.
Want to avoid exception raised due to comparing nodes directly.
See Issue #3493
'''
class Test_Node:
def __init__(self, n):
self.label = n
self.priority = 1
def __repr__(self):
return 'Node({})'.format(self.label)
def sorting_key(node):
return node.priority
test_nodes = [Test_Node(n) for n in range(4)]
G = nx.DiGraph()
edges = [(0, 1), (0, 2), (0, 3), (2, 3)]
G.add_edges_from((test_nodes[a], test_nodes[b]) for a, b in edges)
sorting = list(nx.lexicographical_topological_sort(G, key=sorting_key))
# order reported does depend on order of list(G) in python 3.5
# and that is not deterministic due to dicts not being ordered until v3.6
# after dropping NX support for 3.5 this can become:
# assert_equal(sorting, test_nodes)
assert set(sorting) == set(test_nodes)
def test_is_aperiodic_cycle():
G = nx.DiGraph()
nx.add_cycle(G, [1, 2, 3, 4])
assert not nx.is_aperiodic(G)
def test_is_aperiodic_cycle2():
G = nx.DiGraph()
nx.add_cycle(G, [1, 2, 3, 4])
nx.add_cycle(G, [3, 4, 5, 6, 7])
assert nx.is_aperiodic(G)
def test_is_aperiodic_cycle3():
G = nx.DiGraph()
nx.add_cycle(G, [1, 2, 3, 4])
nx.add_cycle(G, [3, 4, 5, 6])
assert not nx.is_aperiodic(G)
def test_is_aperiodic_cycle4():
G = nx.DiGraph()
nx.add_cycle(G, [1, 2, 3, 4])
G.add_edge(1, 3)
assert nx.is_aperiodic(G)
def test_is_aperiodic_selfloop():
G = nx.DiGraph()
nx.add_cycle(G, [1, 2, 3, 4])
G.add_edge(1, 1)
assert nx.is_aperiodic(G)
def test_is_aperiodic_raise():
G = nx.Graph()
pytest.raises(nx.NetworkXError,
nx.is_aperiodic,
G)
def test_is_aperiodic_bipartite():
# Bipartite graph
G = nx.DiGraph(nx.davis_southern_women_graph())
assert not nx.is_aperiodic(G)
def test_is_aperiodic_rary_tree():
G = nx.full_rary_tree(3, 27, create_using=nx.DiGraph())
assert not nx.is_aperiodic(G)
def test_is_aperiodic_disconnected():
# disconnected graph
G = nx.DiGraph()
nx.add_cycle(G, [1, 2, 3, 4])
nx.add_cycle(G, [5, 6, 7, 8])
assert not nx.is_aperiodic(G)
G.add_edge(1, 3)
G.add_edge(5, 7)
assert nx.is_aperiodic(G)
def test_is_aperiodic_disconnected2():
G = nx.DiGraph()
nx.add_cycle(G, [0, 1, 2])
G.add_edge(3, 3)
assert not nx.is_aperiodic(G)
class TestDagToBranching(object):
"""Unit tests for the :func:`networkx.dag_to_branching` function."""
def test_single_root(self):
"""Tests that a directed acyclic graph with a single degree
zero node produces an arborescence.
"""
G = nx.DiGraph([(0, 1), (0, 2), (1, 3), (2, 3)])
B = nx.dag_to_branching(G)
expected = nx.DiGraph([(0, 1), (1, 3), (0, 2), (2, 4)])
assert nx.is_arborescence(B)
assert nx.is_isomorphic(B, expected)
def test_multiple_roots(self):
"""Tests that a directed acyclic graph with multiple degree zero
nodes creates an arborescence with multiple (weakly) connected
components.
"""
G = nx.DiGraph([(0, 1), (0, 2), (1, 3), (2, 3), (5, 2)])
B = nx.dag_to_branching(G)
expected = nx.DiGraph([(0, 1), (1, 3), (0, 2), (2, 4), (5, 6), (6, 7)])
assert nx.is_branching(B)
assert not nx.is_arborescence(B)
assert nx.is_isomorphic(B, expected)
# # Attributes are not copied by this function. If they were, this would
# # be a good test to uncomment.
# def test_copy_attributes(self):
# """Tests that node attributes are copied in the branching."""
# G = nx.DiGraph([(0, 1), (0, 2), (1, 3), (2, 3)])
# for v in G:
# G.node[v]['label'] = str(v)
# B = nx.dag_to_branching(G)
# # Determine the root node of the branching.
# root = next(v for v, d in B.in_degree() if d == 0)
# assert_equal(B.node[root]['label'], '0')
# children = B[root]
# # Get the left and right children, nodes 1 and 2, respectively.
# left, right = sorted(children, key=lambda v: B.node[v]['label'])
# assert_equal(B.node[left]['label'], '1')
# assert_equal(B.node[right]['label'], '2')
# # Get the left grandchild.
# children = B[left]
# assert_equal(len(children), 1)
# left_grandchild = arbitrary_element(children)
# assert_equal(B.node[left_grandchild]['label'], '3')
# # Get the right grandchild.
# children = B[right]
# assert_equal(len(children), 1)
# right_grandchild = arbitrary_element(children)
# assert_equal(B.node[right_grandchild]['label'], '3')
def test_already_arborescence(self):
"""Tests that a directed acyclic graph that is already an
arborescence produces an isomorphic arborescence as output.
"""
A = nx.balanced_tree(2, 2, create_using=nx.DiGraph())
B = nx.dag_to_branching(A)
assert nx.is_isomorphic(A, B)
def test_already_branching(self):
"""Tests that a directed acyclic graph that is already a
branching produces an isomorphic branching as output.
"""
T1 = nx.balanced_tree(2, 2, create_using=nx.DiGraph())
T2 = nx.balanced_tree(2, 2, create_using=nx.DiGraph())
G = nx.disjoint_union(T1, T2)
B = nx.dag_to_branching(G)
assert nx.is_isomorphic(G, B)
def test_not_acyclic(self):
"""Tests that a non-acyclic graph causes an exception."""
with pytest.raises(nx.HasACycle):
G = nx.DiGraph(pairwise('abc', cyclic=True))
nx.dag_to_branching(G)
def test_undirected(self):
with pytest.raises(nx.NetworkXNotImplemented):
nx.dag_to_branching(nx.Graph())
def test_multigraph(self):
with pytest.raises(nx.NetworkXNotImplemented):
nx.dag_to_branching(nx.MultiGraph())
def test_multidigraph(self):
with pytest.raises(nx.NetworkXNotImplemented):
nx.dag_to_branching(nx.MultiDiGraph())