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

535 lines
17 KiB
Python

import random
import pytest
import networkx as nx
from networkx import convert_node_labels_to_integers as cnlti
from networkx.algorithms.simple_paths import _bidirectional_dijkstra
from networkx.algorithms.simple_paths import _bidirectional_shortest_path
from networkx.utils import arbitrary_element
class TestIsSimplePath(object):
"""Unit tests for the
:func:`networkx.algorithms.simple_paths.is_simple_path` function.
"""
def test_empty_list(self):
"""Tests that the empty list is not a valid path, since there
should be a one-to-one correspondence between paths as lists of
nodes and paths as lists of edges.
"""
G = nx.trivial_graph()
assert not nx.is_simple_path(G, [])
def test_trivial_path(self):
"""Tests that the trivial path, a path of length one, is
considered a simple path in a graph.
"""
G = nx.trivial_graph()
assert nx.is_simple_path(G, [0])
def test_trivial_nonpath(self):
"""Tests that a list whose sole element is an object not in the
graph is not considered a simple path.
"""
G = nx.trivial_graph()
assert not nx.is_simple_path(G, ['not a node'])
def test_simple_path(self):
G = nx.path_graph(2)
assert nx.is_simple_path(G, [0, 1])
def test_non_simple_path(self):
G = nx.path_graph(2)
assert not nx.is_simple_path(G, [0, 1, 0])
def test_cycle(self):
G = nx.cycle_graph(3)
assert not nx.is_simple_path(G, [0, 1, 2, 0])
def test_missing_node(self):
G = nx.path_graph(2)
assert not nx.is_simple_path(G, [0, 2])
def test_directed_path(self):
G = nx.DiGraph([(0, 1), (1, 2)])
assert nx.is_simple_path(G, [0, 1, 2])
def test_directed_non_path(self):
G = nx.DiGraph([(0, 1), (1, 2)])
assert not nx.is_simple_path(G, [2, 1, 0])
def test_directed_cycle(self):
G = nx.DiGraph([(0, 1), (1, 2), (2, 0)])
assert not nx.is_simple_path(G, [0, 1, 2, 0])
def test_multigraph(self):
G = nx.MultiGraph([(0, 1), (0, 1)])
assert nx.is_simple_path(G, [0, 1])
def test_multidigraph(self):
G = nx.MultiDiGraph([(0, 1), (0, 1), (1, 0), (1, 0)])
assert nx.is_simple_path(G, [0, 1])
# Tests for all_simple_paths
def test_all_simple_paths():
G = nx.path_graph(4)
paths = nx.all_simple_paths(G, 0, 3)
assert set(tuple(p) for p in paths) == {(0, 1, 2, 3)}
def test_all_simple_paths_with_two_targets_emits_two_paths():
G = nx.path_graph(4)
G.add_edge(2, 4)
paths = nx.all_simple_paths(G, 0, [3, 4])
assert set(tuple(p) for p in paths) == {(0, 1, 2, 3), (0, 1, 2, 4)}
def test_digraph_all_simple_paths_with_two_targets_emits_two_paths():
G = nx.path_graph(4, create_using=nx.DiGraph())
G.add_edge(2, 4)
paths = nx.all_simple_paths(G, 0, [3, 4])
assert set(tuple(p) for p in paths) == {(0, 1, 2, 3), (0, 1, 2, 4)}
def test_all_simple_paths_with_two_targets_cutoff():
G = nx.path_graph(4)
G.add_edge(2, 4)
paths = nx.all_simple_paths(G, 0, [3, 4], cutoff=3)
assert set(tuple(p) for p in paths) == {(0, 1, 2, 3), (0, 1, 2, 4)}
def test_digraph_all_simple_paths_with_two_targets_cutoff():
G = nx.path_graph(4, create_using=nx.DiGraph())
G.add_edge(2, 4)
paths = nx.all_simple_paths(G, 0, [3, 4], cutoff=3)
assert set(tuple(p) for p in paths) == {(0, 1, 2, 3), (0, 1, 2, 4)}
def test_all_simple_paths_with_two_targets_in_line_emits_two_paths():
G = nx.path_graph(4)
paths = nx.all_simple_paths(G, 0, [2, 3])
assert set(tuple(p) for p in paths) == {(0, 1, 2), (0, 1, 2, 3)}
def test_all_simple_paths_ignores_cycle():
G = nx.cycle_graph(3, create_using=nx.DiGraph())
G.add_edge(1, 3)
paths = nx.all_simple_paths(G, 0, 3)
assert set(tuple(p) for p in paths) == {(0, 1, 3)}
def test_all_simple_paths_with_two_targets_inside_cycle_emits_two_paths():
G = nx.cycle_graph(3, create_using=nx.DiGraph())
G.add_edge(1, 3)
paths = nx.all_simple_paths(G, 0, [2, 3])
assert set(tuple(p) for p in paths) == {(0, 1, 2), (0, 1, 3)}
def test_all_simple_paths_source_target():
G = nx.path_graph(4)
paths = nx.all_simple_paths(G, 1, 1)
assert paths == []
def test_all_simple_paths_cutoff():
G = nx.complete_graph(4)
paths = nx.all_simple_paths(G, 0, 1, cutoff=1)
assert set(tuple(p) for p in paths) == {(0, 1)}
paths = nx.all_simple_paths(G, 0, 1, cutoff=2)
assert set(tuple(p) for p in paths) == {(0, 1), (0, 2, 1), (0, 3, 1)}
def test_all_simple_paths_on_non_trivial_graph():
''' you may need to draw this graph to make sure it is reasonable '''
G = nx.path_graph(5, create_using=nx.DiGraph())
G.add_edges_from([(0, 5), (1, 5), (1, 3), (5, 4), (4, 2), (4, 3)])
paths = nx.all_simple_paths(G, 1, [2, 3])
assert set(tuple(p) for p in paths) == {
(1, 2), (1, 3, 4, 2), (1, 5, 4, 2), (1, 3), (1, 2, 3), (1, 5, 4, 3),
(1, 5, 4, 2, 3)}
paths = nx.all_simple_paths(G, 1, [2, 3], cutoff=3)
assert set(tuple(p) for p in paths) == {
(1, 2), (1, 3, 4, 2), (1, 5, 4, 2), (1, 3), (1, 2, 3), (1, 5, 4, 3)}
paths = nx.all_simple_paths(G, 1, [2, 3], cutoff=2)
assert set(tuple(p) for p in paths) == {(1, 2), (1, 3), (1, 2, 3)}
def test_all_simple_paths_multigraph():
G = nx.MultiGraph([(1, 2), (1, 2)])
paths = nx.all_simple_paths(G, 1, 1)
assert paths == []
nx.add_path(G, [3, 1, 10, 2])
paths = list(nx.all_simple_paths(G, 1, 2))
assert len(paths) == 3
assert set(tuple(p) for p in paths) == {(1, 2), (1, 2), (1, 10, 2)}
def test_all_simple_paths_multigraph_with_cutoff():
G = nx.MultiGraph([(1, 2), (1, 2), (1, 10), (10, 2)])
paths = list(nx.all_simple_paths(G, 1, 2, cutoff=1))
assert len(paths) == 2
assert set(tuple(p) for p in paths) == {(1, 2), (1, 2)}
def test_all_simple_paths_directed():
G = nx.DiGraph()
nx.add_path(G, [1, 2, 3])
nx.add_path(G, [3, 2, 1])
paths = nx.all_simple_paths(G, 1, 3)
assert set(tuple(p) for p in paths) == {(1, 2, 3)}
def test_all_simple_paths_empty():
G = nx.path_graph(4)
paths = nx.all_simple_paths(G, 0, 3, cutoff=2)
assert list(paths) == []
def test_all_simple_paths_corner_cases():
assert list(nx.all_simple_paths(nx.empty_graph(2), 0, 0)) == []
assert list(nx.all_simple_paths(nx.empty_graph(2), 0, 1)) == []
assert list(nx.all_simple_paths(nx.path_graph(9), 0, 8, 0)) == []
def hamiltonian_path(G, source):
source = arbitrary_element(G)
neighbors = set(G[source]) - set([source])
n = len(G)
for target in neighbors:
for path in nx.all_simple_paths(G, source, target):
if len(path) == n:
yield path
def test_hamiltonian_path():
from itertools import permutations
G = nx.complete_graph(4)
paths = [list(p) for p in hamiltonian_path(G, 0)]
exact = [[0] + list(p) for p in permutations([1, 2, 3], 3)]
assert sorted(paths) == sorted(exact)
def test_cutoff_zero():
G = nx.complete_graph(4)
paths = nx.all_simple_paths(G, 0, 3, cutoff=0)
assert list(list(p) for p in paths) == []
paths = nx.all_simple_paths(nx.MultiGraph(G), 0, 3, cutoff=0)
assert list(list(p) for p in paths) == []
def test_source_missing():
with pytest.raises(nx.NodeNotFound):
G = nx.Graph()
nx.add_path(G, [1, 2, 3])
paths = list(nx.all_simple_paths(nx.MultiGraph(G), 0, 3))
def test_target_missing():
with pytest.raises(nx.NodeNotFound):
G = nx.Graph()
nx.add_path(G, [1, 2, 3])
paths = list(nx.all_simple_paths(nx.MultiGraph(G), 1, 4))
# Tests for shortest_simple_paths
def test_shortest_simple_paths():
G = cnlti(nx.grid_2d_graph(4, 4), first_label=1, ordering="sorted")
paths = nx.shortest_simple_paths(G, 1, 12)
assert next(paths) == [1, 2, 3, 4, 8, 12]
assert next(paths) == [1, 5, 6, 7, 8, 12]
assert ([len(path) for path in nx.shortest_simple_paths(G, 1, 12)] ==
sorted([len(path) for path in nx.all_simple_paths(G, 1, 12)]))
def test_shortest_simple_paths_directed():
G = nx.cycle_graph(7, create_using=nx.DiGraph())
paths = nx.shortest_simple_paths(G, 0, 3)
assert [path for path in paths] == [[0, 1, 2, 3]]
def test_Greg_Bernstein():
g1 = nx.Graph()
g1.add_nodes_from(["N0", "N1", "N2", "N3", "N4"])
g1.add_edge("N4", "N1", weight=10.0, capacity=50, name="L5")
g1.add_edge("N4", "N0", weight=7.0, capacity=40, name="L4")
g1.add_edge("N0", "N1", weight=10.0, capacity=45, name="L1")
g1.add_edge("N3", "N0", weight=10.0, capacity=50, name="L0")
g1.add_edge("N2", "N3", weight=12.0, capacity=30, name="L2")
g1.add_edge("N1", "N2", weight=15.0, capacity=42, name="L3")
solution = [['N1', 'N0', 'N3'], ['N1', 'N2', 'N3'], ['N1', 'N4', 'N0', 'N3']]
result = list(nx.shortest_simple_paths(g1, 'N1', 'N3', weight='weight'))
assert result == solution
def test_weighted_shortest_simple_path():
def cost_func(path):
return sum(G.adj[u][v]['weight'] for (u, v) in zip(path, path[1:]))
G = nx.complete_graph(5)
weight = {(u, v): random.randint(1, 100) for (u, v) in G.edges()}
nx.set_edge_attributes(G, weight, 'weight')
cost = 0
for path in nx.shortest_simple_paths(G, 0, 3, weight='weight'):
this_cost = cost_func(path)
assert cost <= this_cost
cost = this_cost
def test_directed_weighted_shortest_simple_path():
def cost_func(path):
return sum(G.adj[u][v]['weight'] for (u, v) in zip(path, path[1:]))
G = nx.complete_graph(5)
G = G.to_directed()
weight = {(u, v): random.randint(1, 100) for (u, v) in G.edges()}
nx.set_edge_attributes(G, weight, 'weight')
cost = 0
for path in nx.shortest_simple_paths(G, 0, 3, weight='weight'):
this_cost = cost_func(path)
assert cost <= this_cost
cost = this_cost
def test_weighted_shortest_simple_path_issue2427():
G = nx.Graph()
G.add_edge('IN', 'OUT', weight=2)
G.add_edge('IN', 'A', weight=1)
G.add_edge('IN', 'B', weight=2)
G.add_edge('B', 'OUT', weight=2)
assert (list(nx.shortest_simple_paths(G, 'IN', 'OUT', weight="weight")) ==
[['IN', 'OUT'], ['IN', 'B', 'OUT']])
G = nx.Graph()
G.add_edge('IN', 'OUT', weight=10)
G.add_edge('IN', 'A', weight=1)
G.add_edge('IN', 'B', weight=1)
G.add_edge('B', 'OUT', weight=1)
assert (list(nx.shortest_simple_paths(G, 'IN', 'OUT', weight="weight")) ==
[['IN', 'B', 'OUT'], ['IN', 'OUT']])
def test_directed_weighted_shortest_simple_path_issue2427():
G = nx.DiGraph()
G.add_edge('IN', 'OUT', weight=2)
G.add_edge('IN', 'A', weight=1)
G.add_edge('IN', 'B', weight=2)
G.add_edge('B', 'OUT', weight=2)
assert (list(nx.shortest_simple_paths(G, 'IN', 'OUT', weight="weight")) ==
[['IN', 'OUT'], ['IN', 'B', 'OUT']])
G = nx.DiGraph()
G.add_edge('IN', 'OUT', weight=10)
G.add_edge('IN', 'A', weight=1)
G.add_edge('IN', 'B', weight=1)
G.add_edge('B', 'OUT', weight=1)
assert (list(nx.shortest_simple_paths(G, 'IN', 'OUT', weight="weight")) ==
[['IN', 'B', 'OUT'], ['IN', 'OUT']])
def test_weight_name():
G = nx.cycle_graph(7)
nx.set_edge_attributes(G, 1, 'weight')
nx.set_edge_attributes(G, 1, 'foo')
G.adj[1][2]['foo'] = 7
paths = list(nx.shortest_simple_paths(G, 0, 3, weight='foo'))
solution = [[0, 6, 5, 4, 3], [0, 1, 2, 3]]
assert paths == solution
def test_ssp_source_missing():
with pytest.raises(nx.NodeNotFound):
G = nx.Graph()
nx.add_path(G, [1, 2, 3])
paths = list(nx.shortest_simple_paths(G, 0, 3))
def test_ssp_target_missing():
with pytest.raises(nx.NodeNotFound):
G = nx.Graph()
nx.add_path(G, [1, 2, 3])
paths = list(nx.shortest_simple_paths(G, 1, 4))
def test_ssp_multigraph():
with pytest.raises(nx.NetworkXNotImplemented):
G = nx.MultiGraph()
nx.add_path(G, [1, 2, 3])
paths = list(nx.shortest_simple_paths(G, 1, 4))
def test_ssp_source_missing():
with pytest.raises(nx.NetworkXNoPath):
G = nx.Graph()
nx.add_path(G, [0, 1, 2])
nx.add_path(G, [3, 4, 5])
paths = list(nx.shortest_simple_paths(G, 0, 3))
def test_bidirectional_shortest_path_restricted_cycle():
cycle = nx.cycle_graph(7)
length, path = _bidirectional_shortest_path(cycle, 0, 3)
assert path == [0, 1, 2, 3]
length, path = _bidirectional_shortest_path(cycle, 0, 3, ignore_nodes=[1])
assert path == [0, 6, 5, 4, 3]
def test_bidirectional_shortest_path_restricted_wheel():
wheel = nx.wheel_graph(6)
length, path = _bidirectional_shortest_path(wheel, 1, 3)
assert path in [[1, 0, 3], [1, 2, 3]]
length, path = _bidirectional_shortest_path(wheel, 1, 3, ignore_nodes=[0])
assert path == [1, 2, 3]
length, path = _bidirectional_shortest_path(wheel, 1, 3, ignore_nodes=[0, 2])
assert path == [1, 5, 4, 3]
length, path = _bidirectional_shortest_path(wheel, 1, 3,
ignore_edges=[(1, 0), (5, 0), (2, 3)])
assert path in [[1, 2, 0, 3], [1, 5, 4, 3]]
def test_bidirectional_shortest_path_restricted_directed_cycle():
directed_cycle = nx.cycle_graph(7, create_using=nx.DiGraph())
length, path = _bidirectional_shortest_path(directed_cycle, 0, 3)
assert path == [0, 1, 2, 3]
pytest.raises(
nx.NetworkXNoPath,
_bidirectional_shortest_path,
directed_cycle,
0, 3,
ignore_nodes=[1],
)
length, path = _bidirectional_shortest_path(directed_cycle, 0, 3,
ignore_edges=[(2, 1)])
assert path == [0, 1, 2, 3]
pytest.raises(
nx.NetworkXNoPath,
_bidirectional_shortest_path,
directed_cycle,
0, 3,
ignore_edges=[(1, 2)],
)
def test_bidirectional_shortest_path_ignore():
G = nx.Graph()
nx.add_path(G, [1, 2])
nx.add_path(G, [1, 3])
nx.add_path(G, [1, 4])
pytest.raises(
nx.NetworkXNoPath,
_bidirectional_shortest_path,
G,
1, 2,
ignore_nodes=[1],
)
pytest.raises(
nx.NetworkXNoPath,
_bidirectional_shortest_path,
G,
1, 2,
ignore_nodes=[2],
)
G = nx.Graph()
nx.add_path(G, [1, 3])
nx.add_path(G, [1, 4])
nx.add_path(G, [3, 2])
pytest.raises(
nx.NetworkXNoPath,
_bidirectional_shortest_path,
G,
1, 2,
ignore_nodes=[1, 2],
)
def validate_path(G, s, t, soln_len, path):
assert path[0] == s
assert path[-1] == t
assert soln_len == sum(G[u][v].get('weight', 1)
for u, v in zip(path[:-1], path[1:]))
def validate_length_path(G, s, t, soln_len, length, path):
assert soln_len == length
validate_path(G, s, t, length, path)
def test_bidirectional_dijksta_restricted():
XG = nx.DiGraph()
XG.add_weighted_edges_from([('s', 'u', 10), ('s', 'x', 5),
('u', 'v', 1), ('u', 'x', 2),
('v', 'y', 1), ('x', 'u', 3),
('x', 'v', 5), ('x', 'y', 2),
('y', 's', 7), ('y', 'v', 6)])
XG3 = nx.Graph()
XG3.add_weighted_edges_from([[0, 1, 2], [1, 2, 12],
[2, 3, 1], [3, 4, 5],
[4, 5, 1], [5, 0, 10]])
validate_length_path(XG, 's', 'v', 9,
*_bidirectional_dijkstra(XG, 's', 'v'))
validate_length_path(XG, 's', 'v', 10,
*_bidirectional_dijkstra(XG, 's', 'v', ignore_nodes=['u']))
validate_length_path(XG, 's', 'v', 11,
*_bidirectional_dijkstra(XG, 's', 'v', ignore_edges=[('s', 'x')]))
pytest.raises(
nx.NetworkXNoPath,
_bidirectional_dijkstra,
XG,
's', 'v',
ignore_nodes=['u'],
ignore_edges=[('s', 'x')],
)
validate_length_path(XG3, 0, 3, 15, *_bidirectional_dijkstra(XG3, 0, 3))
validate_length_path(XG3, 0, 3, 16,
*_bidirectional_dijkstra(XG3, 0, 3, ignore_nodes=[1]))
validate_length_path(XG3, 0, 3, 16,
*_bidirectional_dijkstra(XG3, 0, 3, ignore_edges=[(2, 3)]))
pytest.raises(
nx.NetworkXNoPath,
_bidirectional_dijkstra,
XG3,
0, 3,
ignore_nodes=[1],
ignore_edges=[(5, 4)],
)
def test_bidirectional_dijkstra_no_path():
with pytest.raises(nx.NetworkXNoPath):
G = nx.Graph()
nx.add_path(G, [1, 2, 3])
nx.add_path(G, [4, 5, 6])
path = _bidirectional_dijkstra(G, 1, 6)
def test_bidirectional_dijkstra_ignore():
G = nx.Graph()
nx.add_path(G, [1, 2, 10])
nx.add_path(G, [1, 3, 10])
pytest.raises(
nx.NetworkXNoPath,
_bidirectional_dijkstra,
G,
1, 2,
ignore_nodes=[1],
)
pytest.raises(
nx.NetworkXNoPath,
_bidirectional_dijkstra,
G,
1, 2,
ignore_nodes=[2],
)
pytest.raises(
nx.NetworkXNoPath,
_bidirectional_dijkstra,
G,
1, 2,
ignore_nodes=[1, 2],
)