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# Jordi Torrents
# Test for k-cutsets
import itertools
import pytest
import networkx as nx
from networkx.algorithms import flow
from networkx.algorithms.connectivity.kcutsets import _is_separating_set
MAX_CUTSETS_TO_TEST = 4 # originally 100. cut to decrease testing time
flow_funcs = [
flow.boykov_kolmogorov,
flow.dinitz,
flow.edmonds_karp,
flow.preflow_push,
flow.shortest_augmenting_path,
]
##
# Some nice synthetic graphs
##
def graph_example_1():
G = nx.convert_node_labels_to_integers(
nx.grid_graph([5, 5]), label_attribute="labels"
)
rlabels = nx.get_node_attributes(G, "labels")
labels = {v: k for k, v in rlabels.items()}
for nodes in [
(labels[(0, 0)], labels[(1, 0)]),
(labels[(0, 4)], labels[(1, 4)]),
(labels[(3, 0)], labels[(4, 0)]),
(labels[(3, 4)], labels[(4, 4)]),
]:
new_node = G.order() + 1
# Petersen graph is triconnected
P = nx.petersen_graph()
G = nx.disjoint_union(G, P)
# Add two edges between the grid and P
G.add_edge(new_node + 1, nodes[0])
G.add_edge(new_node, nodes[1])
# K5 is 4-connected
K = nx.complete_graph(5)
G = nx.disjoint_union(G, K)
# Add three edges between P and K5
G.add_edge(new_node + 2, new_node + 11)
G.add_edge(new_node + 3, new_node + 12)
G.add_edge(new_node + 4, new_node + 13)
# Add another K5 sharing a node
G = nx.disjoint_union(G, K)
nbrs = G[new_node + 10]
G.remove_node(new_node + 10)
for nbr in nbrs:
G.add_edge(new_node + 17, nbr)
G.add_edge(new_node + 16, new_node + 5)
return G
def torrents_and_ferraro_graph():
G = nx.convert_node_labels_to_integers(
nx.grid_graph([5, 5]), label_attribute="labels"
)
rlabels = nx.get_node_attributes(G, "labels")
labels = {v: k for k, v in rlabels.items()}
for nodes in [(labels[(0, 4)], labels[(1, 4)]), (labels[(3, 4)], labels[(4, 4)])]:
new_node = G.order() + 1
# Petersen graph is triconnected
P = nx.petersen_graph()
G = nx.disjoint_union(G, P)
# Add two edges between the grid and P
G.add_edge(new_node + 1, nodes[0])
G.add_edge(new_node, nodes[1])
# K5 is 4-connected
K = nx.complete_graph(5)
G = nx.disjoint_union(G, K)
# Add three edges between P and K5
G.add_edge(new_node + 2, new_node + 11)
G.add_edge(new_node + 3, new_node + 12)
G.add_edge(new_node + 4, new_node + 13)
# Add another K5 sharing a node
G = nx.disjoint_union(G, K)
nbrs = G[new_node + 10]
G.remove_node(new_node + 10)
for nbr in nbrs:
G.add_edge(new_node + 17, nbr)
# Commenting this makes the graph not biconnected !!
# This stupid mistake make one reviewer very angry :P
G.add_edge(new_node + 16, new_node + 8)
for nodes in [(labels[(0, 0)], labels[(1, 0)]), (labels[(3, 0)], labels[(4, 0)])]:
new_node = G.order() + 1
# Petersen graph is triconnected
P = nx.petersen_graph()
G = nx.disjoint_union(G, P)
# Add two edges between the grid and P
G.add_edge(new_node + 1, nodes[0])
G.add_edge(new_node, nodes[1])
# K5 is 4-connected
K = nx.complete_graph(5)
G = nx.disjoint_union(G, K)
# Add three edges between P and K5
G.add_edge(new_node + 2, new_node + 11)
G.add_edge(new_node + 3, new_node + 12)
G.add_edge(new_node + 4, new_node + 13)
# Add another K5 sharing two nodes
G = nx.disjoint_union(G, K)
nbrs = G[new_node + 10]
G.remove_node(new_node + 10)
for nbr in nbrs:
G.add_edge(new_node + 17, nbr)
nbrs2 = G[new_node + 9]
G.remove_node(new_node + 9)
for nbr in nbrs2:
G.add_edge(new_node + 18, nbr)
return G
# Helper function
def _check_separating_sets(G):
for cc in nx.connected_components(G):
if len(cc) < 3:
continue
Gc = G.subgraph(cc)
node_conn = nx.node_connectivity(Gc)
all_cuts = nx.all_node_cuts(Gc)
# Only test a limited number of cut sets to reduce test time.
for cut in itertools.islice(all_cuts, MAX_CUTSETS_TO_TEST):
assert node_conn == len(cut)
assert not nx.is_connected(nx.restricted_view(G, cut, []))
@pytest.mark.slow
def test_torrents_and_ferraro_graph():
G = torrents_and_ferraro_graph()
_check_separating_sets(G)
def test_example_1():
G = graph_example_1()
_check_separating_sets(G)
def test_random_gnp():
G = nx.gnp_random_graph(100, 0.1, seed=42)
_check_separating_sets(G)
def test_shell():
constructor = [(20, 80, 0.8), (80, 180, 0.6)]
G = nx.random_shell_graph(constructor, seed=42)
_check_separating_sets(G)
def test_configuration():
deg_seq = nx.random_powerlaw_tree_sequence(100, tries=5, seed=72)
G = nx.Graph(nx.configuration_model(deg_seq))
G.remove_edges_from(nx.selfloop_edges(G))
_check_separating_sets(G)
def test_karate():
G = nx.karate_club_graph()
_check_separating_sets(G)
def _generate_no_biconnected(max_attempts=50):
attempts = 0
while True:
G = nx.fast_gnp_random_graph(100, 0.0575, seed=42)
if nx.is_connected(G) and not nx.is_biconnected(G):
attempts = 0
yield G
else:
if attempts >= max_attempts:
msg = f"Tried {attempts} times: no suitable Graph."
raise Exception(msg)
else:
attempts += 1
def test_articulation_points():
Ggen = _generate_no_biconnected()
for i in range(1): # change 1 to 3 or more for more realizations.
G = next(Ggen)
articulation_points = [{a} for a in nx.articulation_points(G)]
for cut in nx.all_node_cuts(G):
assert cut in articulation_points
def test_grid_2d_graph():
# All minimum node cuts of a 2d grid
# are the four pairs of nodes that are
# neighbors of the four corner nodes.
G = nx.grid_2d_graph(5, 5)
solution = [{(0, 1), (1, 0)}, {(3, 0), (4, 1)}, {(3, 4), (4, 3)}, {(0, 3), (1, 4)}]
for cut in nx.all_node_cuts(G):
assert cut in solution
def test_disconnected_graph():
G = nx.fast_gnp_random_graph(100, 0.01, seed=42)
cuts = nx.all_node_cuts(G)
pytest.raises(nx.NetworkXError, next, cuts)
@pytest.mark.slow
def test_alternative_flow_functions():
graphs = [nx.grid_2d_graph(4, 4), nx.cycle_graph(5)]
for G in graphs:
node_conn = nx.node_connectivity(G)
for flow_func in flow_funcs:
all_cuts = nx.all_node_cuts(G, flow_func=flow_func)
# Only test a limited number of cut sets to reduce test time.
for cut in itertools.islice(all_cuts, MAX_CUTSETS_TO_TEST):
assert node_conn == len(cut)
assert not nx.is_connected(nx.restricted_view(G, cut, []))
def test_is_separating_set_complete_graph():
G = nx.complete_graph(5)
assert _is_separating_set(G, {0, 1, 2, 3})
def test_is_separating_set():
for i in [5, 10, 15]:
G = nx.star_graph(i)
max_degree_node = max(G, key=G.degree)
assert _is_separating_set(G, {max_degree_node})
def test_non_repeated_cuts():
# The algorithm was repeating the cut {0, 1} for the giant biconnected
# component of the Karate club graph.
K = nx.karate_club_graph()
bcc = max(list(nx.biconnected_components(K)), key=len)
G = K.subgraph(bcc)
solution = [{32, 33}, {2, 33}, {0, 3}, {0, 1}, {29, 33}]
cuts = list(nx.all_node_cuts(G))
if len(solution) != len(cuts):
print(f"Solution: {solution}")
print(f"Result: {cuts}")
assert len(solution) == len(cuts)
for cut in cuts:
assert cut in solution
def test_cycle_graph():
G = nx.cycle_graph(5)
solution = [{0, 2}, {0, 3}, {1, 3}, {1, 4}, {2, 4}]
cuts = list(nx.all_node_cuts(G))
assert len(solution) == len(cuts)
for cut in cuts:
assert cut in solution
def test_complete_graph():
G = nx.complete_graph(5)
assert nx.node_connectivity(G) == 4
assert list(nx.all_node_cuts(G)) == []
def test_all_node_cuts_simple_case():
G = nx.complete_graph(5)
G.remove_edges_from([(0, 1), (3, 4)])
expected = [{0, 1, 2}, {2, 3, 4}]
actual = list(nx.all_node_cuts(G))
assert len(actual) == len(expected)
for cut in actual:
assert cut in expected
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