1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
|
import pytest
import networkx as nx
from networkx.algorithms import flow
from networkx.algorithms.connectivity import minimum_st_edge_cut, minimum_st_node_cut
from networkx.utils import arbitrary_element
flow_funcs = [
flow.boykov_kolmogorov,
flow.dinitz,
flow.edmonds_karp,
flow.preflow_push,
flow.shortest_augmenting_path,
]
# Tests for node and edge cutsets
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 flow_func in flow_funcs:
errmsg = f"Assertion failed in function: {flow_func.__name__}"
for i in range(1): # change 1 to 3 or more for more realizations.
G = next(Ggen)
cut = nx.minimum_node_cut(G, flow_func=flow_func)
assert len(cut) == 1, errmsg
assert cut.pop() in set(nx.articulation_points(G)), errmsg
def test_brandes_erlebach_book():
# Figure 1 chapter 7: Connectivity
# http://www.informatik.uni-augsburg.de/thi/personen/kammer/Graph_Connectivity.pdf
G = nx.Graph()
G.add_edges_from(
[
(1, 2),
(1, 3),
(1, 4),
(1, 5),
(2, 3),
(2, 6),
(3, 4),
(3, 6),
(4, 6),
(4, 7),
(5, 7),
(6, 8),
(6, 9),
(7, 8),
(7, 10),
(8, 11),
(9, 10),
(9, 11),
(10, 11),
]
)
for flow_func in flow_funcs:
kwargs = {"flow_func": flow_func}
errmsg = f"Assertion failed in function: {flow_func.__name__}"
# edge cutsets
assert 3 == len(nx.minimum_edge_cut(G, 1, 11, **kwargs)), errmsg
edge_cut = nx.minimum_edge_cut(G, **kwargs)
# Node 5 has only two edges
assert 2 == len(edge_cut), errmsg
H = G.copy()
H.remove_edges_from(edge_cut)
assert not nx.is_connected(H), errmsg
# node cuts
assert {6, 7} == minimum_st_node_cut(G, 1, 11, **kwargs), errmsg
assert {6, 7} == nx.minimum_node_cut(G, 1, 11, **kwargs), errmsg
node_cut = nx.minimum_node_cut(G, **kwargs)
assert 2 == len(node_cut), errmsg
H = G.copy()
H.remove_nodes_from(node_cut)
assert not nx.is_connected(H), errmsg
def test_white_harary_paper():
# Figure 1b white and harary (2001)
# https://doi.org/10.1111/0081-1750.00098
# A graph with high adhesion (edge connectivity) and low cohesion
# (node connectivity)
G = nx.disjoint_union(nx.complete_graph(4), nx.complete_graph(4))
G.remove_node(7)
for i in range(4, 7):
G.add_edge(0, i)
G = nx.disjoint_union(G, nx.complete_graph(4))
G.remove_node(G.order() - 1)
for i in range(7, 10):
G.add_edge(0, i)
for flow_func in flow_funcs:
kwargs = {"flow_func": flow_func}
errmsg = f"Assertion failed in function: {flow_func.__name__}"
# edge cuts
edge_cut = nx.minimum_edge_cut(G, **kwargs)
assert 3 == len(edge_cut), errmsg
H = G.copy()
H.remove_edges_from(edge_cut)
assert not nx.is_connected(H), errmsg
# node cuts
node_cut = nx.minimum_node_cut(G, **kwargs)
assert {0} == node_cut, errmsg
H = G.copy()
H.remove_nodes_from(node_cut)
assert not nx.is_connected(H), errmsg
def test_petersen_cutset():
G = nx.petersen_graph()
for flow_func in flow_funcs:
kwargs = {"flow_func": flow_func}
errmsg = f"Assertion failed in function: {flow_func.__name__}"
# edge cuts
edge_cut = nx.minimum_edge_cut(G, **kwargs)
assert 3 == len(edge_cut), errmsg
H = G.copy()
H.remove_edges_from(edge_cut)
assert not nx.is_connected(H), errmsg
# node cuts
node_cut = nx.minimum_node_cut(G, **kwargs)
assert 3 == len(node_cut), errmsg
H = G.copy()
H.remove_nodes_from(node_cut)
assert not nx.is_connected(H), errmsg
def test_octahedral_cutset():
G = nx.octahedral_graph()
for flow_func in flow_funcs:
kwargs = {"flow_func": flow_func}
errmsg = f"Assertion failed in function: {flow_func.__name__}"
# edge cuts
edge_cut = nx.minimum_edge_cut(G, **kwargs)
assert 4 == len(edge_cut), errmsg
H = G.copy()
H.remove_edges_from(edge_cut)
assert not nx.is_connected(H), errmsg
# node cuts
node_cut = nx.minimum_node_cut(G, **kwargs)
assert 4 == len(node_cut), errmsg
H = G.copy()
H.remove_nodes_from(node_cut)
assert not nx.is_connected(H), errmsg
def test_icosahedral_cutset():
G = nx.icosahedral_graph()
for flow_func in flow_funcs:
kwargs = {"flow_func": flow_func}
errmsg = f"Assertion failed in function: {flow_func.__name__}"
# edge cuts
edge_cut = nx.minimum_edge_cut(G, **kwargs)
assert 5 == len(edge_cut), errmsg
H = G.copy()
H.remove_edges_from(edge_cut)
assert not nx.is_connected(H), errmsg
# node cuts
node_cut = nx.minimum_node_cut(G, **kwargs)
assert 5 == len(node_cut), errmsg
H = G.copy()
H.remove_nodes_from(node_cut)
assert not nx.is_connected(H), errmsg
def test_node_cutset_exception():
G = nx.Graph()
G.add_edges_from([(1, 2), (3, 4)])
for flow_func in flow_funcs:
pytest.raises(nx.NetworkXError, nx.minimum_node_cut, G, flow_func=flow_func)
def test_node_cutset_random_graphs():
for flow_func in flow_funcs:
errmsg = f"Assertion failed in function: {flow_func.__name__}"
for i in range(3):
G = nx.fast_gnp_random_graph(50, 0.25, seed=42)
if not nx.is_connected(G):
ccs = iter(nx.connected_components(G))
start = arbitrary_element(next(ccs))
G.add_edges_from((start, arbitrary_element(c)) for c in ccs)
cutset = nx.minimum_node_cut(G, flow_func=flow_func)
assert nx.node_connectivity(G) == len(cutset), errmsg
G.remove_nodes_from(cutset)
assert not nx.is_connected(G), errmsg
def test_edge_cutset_random_graphs():
for flow_func in flow_funcs:
errmsg = f"Assertion failed in function: {flow_func.__name__}"
for i in range(3):
G = nx.fast_gnp_random_graph(50, 0.25, seed=42)
if not nx.is_connected(G):
ccs = iter(nx.connected_components(G))
start = arbitrary_element(next(ccs))
G.add_edges_from((start, arbitrary_element(c)) for c in ccs)
cutset = nx.minimum_edge_cut(G, flow_func=flow_func)
assert nx.edge_connectivity(G) == len(cutset), errmsg
G.remove_edges_from(cutset)
assert not nx.is_connected(G), errmsg
def test_empty_graphs():
G = nx.Graph()
D = nx.DiGraph()
for interface_func in [nx.minimum_node_cut, nx.minimum_edge_cut]:
for flow_func in flow_funcs:
pytest.raises(
nx.NetworkXPointlessConcept, interface_func, G, flow_func=flow_func
)
pytest.raises(
nx.NetworkXPointlessConcept, interface_func, D, flow_func=flow_func
)
def test_unbounded():
G = nx.complete_graph(5)
for flow_func in flow_funcs:
assert 4 == len(minimum_st_edge_cut(G, 1, 4, flow_func=flow_func))
def test_missing_source():
G = nx.path_graph(4)
for interface_func in [nx.minimum_edge_cut, nx.minimum_node_cut]:
for flow_func in flow_funcs:
pytest.raises(
nx.NetworkXError, interface_func, G, 10, 1, flow_func=flow_func
)
def test_missing_target():
G = nx.path_graph(4)
for interface_func in [nx.minimum_edge_cut, nx.minimum_node_cut]:
for flow_func in flow_funcs:
pytest.raises(
nx.NetworkXError, interface_func, G, 1, 10, flow_func=flow_func
)
def test_not_weakly_connected():
G = nx.DiGraph()
nx.add_path(G, [1, 2, 3])
nx.add_path(G, [4, 5])
for interface_func in [nx.minimum_edge_cut, nx.minimum_node_cut]:
for flow_func in flow_funcs:
pytest.raises(nx.NetworkXError, interface_func, G, flow_func=flow_func)
def test_not_connected():
G = nx.Graph()
nx.add_path(G, [1, 2, 3])
nx.add_path(G, [4, 5])
for interface_func in [nx.minimum_edge_cut, nx.minimum_node_cut]:
for flow_func in flow_funcs:
pytest.raises(nx.NetworkXError, interface_func, G, flow_func=flow_func)
def tests_min_cut_complete():
G = nx.complete_graph(5)
for interface_func in [nx.minimum_edge_cut, nx.minimum_node_cut]:
for flow_func in flow_funcs:
assert 4 == len(interface_func(G, flow_func=flow_func))
def tests_min_cut_complete_directed():
G = nx.complete_graph(5)
G = G.to_directed()
for interface_func in [nx.minimum_edge_cut, nx.minimum_node_cut]:
for flow_func in flow_funcs:
assert 4 == len(interface_func(G, flow_func=flow_func))
def tests_minimum_st_node_cut():
G = nx.Graph()
G.add_nodes_from([0, 1, 2, 3, 7, 8, 11, 12])
G.add_edges_from([(7, 11), (1, 11), (1, 12), (12, 8), (0, 1)])
nodelist = minimum_st_node_cut(G, 7, 11)
assert nodelist == {}
def test_invalid_auxiliary():
G = nx.complete_graph(5)
pytest.raises(nx.NetworkXError, minimum_st_node_cut, G, 0, 3, auxiliary=G)
def test_interface_only_source():
G = nx.complete_graph(5)
for interface_func in [nx.minimum_node_cut, nx.minimum_edge_cut]:
pytest.raises(nx.NetworkXError, interface_func, G, s=0)
def test_interface_only_target():
G = nx.complete_graph(5)
for interface_func in [nx.minimum_node_cut, nx.minimum_edge_cut]:
pytest.raises(nx.NetworkXError, interface_func, G, t=3)
|
