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
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
|
import unittest
from random import shuffle
from igraph import Graph
def node_compat(g1, g2, v1, v2):
"""Node compatibility function for isomorphism tests"""
return g1.vs[v1]["color"] == g2.vs[v2]["color"]
def edge_compat(g1, g2, e1, e2):
"""Edge compatibility function for isomorphism tests"""
return g1.es[e1]["color"] == g2.es[e2]["color"]
class IsomorphismTests(unittest.TestCase):
def testIsomorphic(self):
g1 = Graph(
8,
[
(0, 4),
(0, 5),
(0, 6),
(1, 4),
(1, 5),
(1, 7),
(2, 4),
(2, 6),
(2, 7),
(3, 5),
(3, 6),
(3, 7),
],
)
g2 = Graph(
8,
[
(0, 1),
(0, 3),
(0, 4),
(2, 3),
(2, 1),
(2, 6),
(5, 1),
(5, 4),
(5, 6),
(7, 3),
(7, 6),
(7, 4),
],
)
# Test the isomorphism of g1 and g2
self.assertTrue(g1.isomorphic(g2))
self.assertTrue(
g2.isomorphic_vf2(g1, return_mapping_21=True)
== (True, None, [0, 2, 5, 7, 1, 3, 4, 6])
)
self.assertTrue(
g2.isomorphic_bliss(g1, return_mapping_21=True, sh1="fl")
== (True, None, [0, 2, 5, 7, 1, 3, 4, 6])
)
self.assertRaises(ValueError, g2.isomorphic_bliss, g1, sh2="nonexistent")
# Test the automorphy of g1
self.assertTrue(g1.isomorphic())
self.assertTrue(
g1.isomorphic_vf2(return_mapping_21=True)
== (True, None, [0, 1, 2, 3, 4, 5, 6, 7])
)
# Test VF2 with colors
self.assertTrue(
g1.isomorphic_vf2(
g2, color1=[0, 1, 0, 1, 0, 1, 0, 1], color2=[0, 0, 1, 1, 0, 0, 1, 1]
)
)
g1.vs["color"] = [0, 1, 0, 1, 0, 1, 0, 1]
g2.vs["color"] = [0, 0, 1, 1, 0, 1, 1, 0]
self.assertTrue(not g1.isomorphic_vf2(g2, "color", "color"))
# Test bliss with colors
self.assertTrue(
g1.isomorphic_bliss(
g2, color1=[0, 0, 0, 0, 0, 0, 0, 0], color2=[0, 0, 0, 0, 0, 0, 0, 0]
)
)
self.assertTrue(
g1.isomorphic_bliss(
g2, color1=[1, 0, 2, 0, 0, 0, 0, 0], color2=[1, 0, 2, 0, 0, 0, 0, 0]
)
)
self.assertTrue(
g1.isomorphic_bliss(
g2, color1=[0, 1, 0, 1, 0, 1, 0, 1], color2=[0, 0, 1, 1, 0, 0, 1, 1]
)
)
# Test VF2 with vertex and edge colors
self.assertTrue(
g1.isomorphic_vf2(
g2, color1=[0, 1, 0, 1, 0, 1, 0, 1], color2=[0, 0, 1, 1, 0, 0, 1, 1]
)
)
g1.es["color"] = list(range(12))
g2.es["color"] = [0] * 6 + [1] * 6
self.assertTrue(not g1.isomorphic_vf2(g2, "color", "color", "color", "color"))
# Test VF2 with node compatibility function
g2.vs["color"] = [0, 0, 1, 1, 0, 0, 1, 1]
self.assertTrue(g1.isomorphic_vf2(g2, node_compat_fn=node_compat))
g2.vs["color"] = [0, 0, 1, 1, 0, 1, 1, 0]
self.assertTrue(not g1.isomorphic_vf2(g2, node_compat_fn=node_compat))
# Test VF2 with node edge compatibility function
g2.vs["color"] = [0, 0, 1, 1, 0, 0, 1, 1]
g1.es["color"] = list(range(12))
g2.es["color"] = [0] * 6 + [1] * 6
self.assertTrue(
not g1.isomorphic_vf2(
g2, node_compat_fn=node_compat, edge_compat_fn=edge_compat
)
)
def testIsomorphicCallback(self):
maps = []
def callback(g1, g2, map1, map2):
maps.append(map1)
return True
# Test VF2 callback
g = Graph(6, [(0, 1), (2, 3), (4, 5), (0, 2), (2, 4), (1, 3), (3, 5)])
g.isomorphic_vf2(g, callback=callback)
expected_maps = [
[0, 1, 2, 3, 4, 5],
[1, 0, 3, 2, 5, 4],
[4, 5, 2, 3, 0, 1],
[5, 4, 3, 2, 1, 0],
]
self.assertTrue(sorted(maps) == expected_maps)
maps[:] = []
g3 = Graph.Full(4)
g3.vs["color"] = [0, 1, 1, 0]
g3.isomorphic_vf2(callback=callback, color1="color", color2="color")
expected_maps = [[0, 1, 2, 3], [0, 2, 1, 3], [3, 1, 2, 0], [3, 2, 1, 0]]
self.assertTrue(sorted(maps) == expected_maps)
def testCountIsomorphisms(self):
g = Graph.Full(4)
self.assertTrue(g.count_automorphisms_vf2() == 24)
g = Graph(6, [(0, 1), (2, 3), (4, 5), (0, 2), (2, 4), (1, 3), (3, 5)])
self.assertTrue(g.count_automorphisms_vf2() == 4)
# Some more tests with colors
g3 = Graph.Full(4)
g3.vs["color"] = [0, 1, 1, 0]
self.assertTrue(g3.count_isomorphisms_vf2() == 24)
self.assertTrue(g3.count_isomorphisms_vf2(color1="color", color2="color") == 4)
self.assertTrue(
g3.count_isomorphisms_vf2(color1=[0, 1, 2, 0], color2=(0, 1, 2, 0)) == 2
)
self.assertTrue(
g3.count_isomorphisms_vf2(
edge_color1=[0, 1, 0, 0, 0, 1], edge_color2=[0, 1, 0, 0, 0, 1]
)
== 2
)
# Test VF2 with node/edge compatibility function
g3.vs["color"] = [0, 1, 1, 0]
self.assertTrue(g3.count_isomorphisms_vf2(node_compat_fn=node_compat) == 4)
g3.vs["color"] = [0, 1, 2, 0]
self.assertTrue(g3.count_isomorphisms_vf2(node_compat_fn=node_compat) == 2)
g3.es["color"] = [0, 1, 0, 0, 0, 1]
self.assertTrue(g3.count_isomorphisms_vf2(edge_compat_fn=edge_compat) == 2)
def testGetIsomorphisms(self):
g = Graph(6, [(0, 1), (2, 3), (4, 5), (0, 2), (2, 4), (1, 3), (3, 5)])
maps = g.get_automorphisms_vf2()
expected_maps = [
[0, 1, 2, 3, 4, 5],
[1, 0, 3, 2, 5, 4],
[4, 5, 2, 3, 0, 1],
[5, 4, 3, 2, 1, 0],
]
self.assertTrue(maps == expected_maps)
g3 = Graph.Full(4)
g3.vs["color"] = [0, 1, 1, 0]
expected_maps = [[0, 1, 2, 3], [0, 2, 1, 3], [3, 1, 2, 0], [3, 2, 1, 0]]
self.assertTrue(
sorted(g3.get_automorphisms_vf2(color="color")) == expected_maps
)
class SubisomorphismTests(unittest.TestCase):
def testSubisomorphicLAD(self):
g = Graph.Lattice([3, 3], circular=False)
g2 = Graph([(0, 1), (1, 2), (1, 3)])
g3 = g + [(0, 4), (2, 4), (6, 4), (8, 4), (3, 1), (1, 5), (5, 7), (7, 3)]
self.assertTrue(g.subisomorphic_lad(g2))
self.assertFalse(g2.subisomorphic_lad(g))
# Test 'induced'
self.assertFalse(g3.subisomorphic_lad(g, induced=True))
self.assertTrue(g3.subisomorphic_lad(g, induced=False))
self.assertTrue(g3.subisomorphic_lad(g))
self.assertTrue(g3.subisomorphic_lad(g2, induced=True))
self.assertTrue(g3.subisomorphic_lad(g2, induced=False))
self.assertTrue(g3.subisomorphic_lad(g2))
# Test with limited vertex matching
domains = [
[4],
[0, 1, 2, 3, 5, 6, 7, 8],
[0, 1, 2, 3, 5, 6, 7, 8],
[0, 1, 2, 3, 5, 6, 7, 8],
]
self.assertTrue(g.subisomorphic_lad(g2, domains=domains))
domains = [
[],
[0, 1, 2, 3, 5, 6, 7, 8],
[0, 1, 2, 3, 5, 6, 7, 8],
[0, 1, 2, 3, 5, 6, 7, 8],
]
self.assertTrue(not g.subisomorphic_lad(g2, domains=domains))
# Corner cases
empty = Graph()
self.assertTrue(g.subisomorphic_lad(empty))
self.assertTrue(empty.subisomorphic_lad(empty))
def testGetSubisomorphismsLAD(self):
g = Graph.Lattice([3, 3], circular=False)
g2 = Graph([(0, 1), (1, 2), (2, 3), (3, 0)])
g3 = g + [(0, 4), (2, 4), (6, 4), (8, 4), (3, 1), (1, 5), (5, 7), (7, 3)]
all_subiso = "0143 0341 1034 1254 1430 1452 2145 2541 3014 3410 3476 \
3674 4103 4125 4301 4367 4521 4587 4763 4785 5214 5412 5478 5874 6347 \
6743 7436 7458 7634 7854 8547 8745"
all_subiso = sorted([int(x) for x in item] for item in all_subiso.split())
self.assertEqual(all_subiso, sorted(g.get_subisomorphisms_lad(g2)))
self.assertEqual([], sorted(g2.get_subisomorphisms_lad(g)))
# Test 'induced'
induced_subiso = "1375 1573 3751 5731 7513 7315 5137 3157"
induced_subiso = sorted(
[int(x) for x in item] for item in induced_subiso.split()
)
self.assertEqual(
induced_subiso, sorted(g3.get_subisomorphisms_lad(g2, induced=True))
)
self.assertEqual([], g3.get_subisomorphisms_lad(g, induced=True))
# Test with limited vertex matching
limited_subiso = [iso for iso in all_subiso if iso[0] == 4]
domains = [
[4],
[0, 1, 2, 3, 5, 6, 7, 8],
[0, 1, 2, 3, 5, 6, 7, 8],
[0, 1, 2, 3, 5, 6, 7, 8],
]
self.assertEqual(
limited_subiso, sorted(g.get_subisomorphisms_lad(g2, domains=domains))
)
domains = [
[],
[0, 1, 2, 3, 5, 6, 7, 8],
[0, 1, 2, 3, 5, 6, 7, 8],
[0, 1, 2, 3, 5, 6, 7, 8],
]
self.assertEqual([], sorted(g.get_subisomorphisms_lad(g2, domains=domains)))
# Corner cases
empty = Graph()
self.assertEqual([[]], g.get_subisomorphisms_lad(empty))
self.assertEqual([[]], empty.get_subisomorphisms_lad(empty))
def testSubisomorphicVF2(self):
g = Graph.Lattice([3, 3], circular=False)
g2 = Graph([(0, 1), (1, 2), (1, 3)])
self.assertTrue(g.subisomorphic_vf2(g2))
self.assertTrue(not g2.subisomorphic_vf2(g))
# Test with vertex colors
g.vs["color"] = [0, 0, 0, 0, 1, 0, 0, 0, 0]
g2.vs["color"] = [1, 0, 0, 0]
self.assertTrue(g.subisomorphic_vf2(g2, node_compat_fn=node_compat))
g2.vs["color"] = [2, 0, 0, 0]
self.assertTrue(not g.subisomorphic_vf2(g2, node_compat_fn=node_compat))
# Test with edge colors
g.es["color"] = [1] + [0] * (g.ecount() - 1)
g2.es["color"] = [1] + [0] * (g2.ecount() - 1)
self.assertTrue(g.subisomorphic_vf2(g2, edge_compat_fn=edge_compat))
g2.es[0]["color"] = [2]
self.assertTrue(not g.subisomorphic_vf2(g2, node_compat_fn=node_compat))
def testCountSubisomorphisms(self):
g = Graph.Lattice([3, 3], circular=False)
g2 = Graph.Lattice([2, 2], circular=False)
self.assertTrue(g.count_subisomorphisms_vf2(g2) == 4 * 4 * 2)
self.assertTrue(g2.count_subisomorphisms_vf2(g) == 0)
# Test with vertex colors
g.vs["color"] = [0, 0, 0, 0, 1, 0, 0, 0, 0]
g2.vs["color"] = [1, 0, 0, 0]
self.assertTrue(g.count_subisomorphisms_vf2(g2, "color", "color") == 4 * 2)
self.assertTrue(
g.count_subisomorphisms_vf2(g2, node_compat_fn=node_compat) == 4 * 2
)
# Test with edge colors
g.es["color"] = [1] + [0] * (g.ecount() - 1)
g2.es["color"] = [1] + [0] * (g2.ecount() - 1)
self.assertTrue(
g.count_subisomorphisms_vf2(g2, edge_color1="color", edge_color2="color")
== 2
)
self.assertTrue(
g.count_subisomorphisms_vf2(g2, edge_compat_fn=edge_compat) == 2
)
class PermutationTests(unittest.TestCase):
def testCanonicalPermutation(self):
# Simple case: two ring graphs
g1 = Graph(4, [(0, 1), (1, 2), (2, 3), (3, 0)])
g2 = Graph(4, [(0, 1), (1, 3), (3, 2), (2, 0)])
cp = g1.canonical_permutation()
g3 = g1.permute_vertices(cp)
cp = g2.canonical_permutation()
g4 = g2.permute_vertices(cp)
self.assertTrue(g3.vcount() == g4.vcount())
self.assertTrue(sorted(g3.get_edgelist()) == sorted(g4.get_edgelist()))
# Simple case with coloring
cp = g1.canonical_permutation(color=[0, 0, 1, 1])
g3 = g1.permute_vertices(cp)
cp = g2.canonical_permutation(color=[0, 0, 1, 1])
g4 = g2.permute_vertices(cp)
self.assertTrue(g3.vcount() == g4.vcount())
self.assertTrue(sorted(g3.get_edgelist()) == sorted(g4.get_edgelist()))
# More complicated one: small GRG, random permutation
g = Graph.GRG(10, 0.5)
perm = list(range(10))
shuffle(perm)
g2 = g.permute_vertices(perm)
g3 = g.permute_vertices(g.canonical_permutation())
g4 = g2.permute_vertices(g2.canonical_permutation())
self.assertTrue(g3.vcount() == g4.vcount())
self.assertTrue(sorted(g3.get_edgelist()) == sorted(g4.get_edgelist()))
def testPermuteVertices(self):
g1 = Graph(
8,
[
(0, 4),
(0, 5),
(0, 6),
(1, 4),
(1, 5),
(1, 7),
(2, 4),
(2, 6),
(2, 7),
(3, 5),
(3, 6),
(3, 7),
],
)
g2 = Graph(
8,
[
(0, 1),
(0, 3),
(0, 4),
(2, 3),
(2, 1),
(2, 6),
(5, 1),
(5, 4),
(5, 6),
(7, 3),
(7, 6),
(7, 4),
],
)
_, _, mapping = g1.isomorphic_vf2(g2, return_mapping_21=True)
g3 = g2.permute_vertices(mapping)
self.assertTrue(g3.vcount() == g2.vcount() and g3.ecount() == g2.ecount())
self.assertTrue(set(g3.get_edgelist()) == set(g1.get_edgelist()))
class AutomorphismTests(unittest.TestCase):
def testCountAutomorphisms(self):
g = Graph.Famous("petersen")
self.assertEqual(120, g.count_automorphisms())
g = Graph.Lattice([16, 16])
self.assertEqual(2048, g.count_automorphisms())
def testAutomorphismGroup(self):
g = Graph.Famous("petersen")
generators = g.automorphism_group()
generators.sort()
self.assertEqual(
generators,
[
[0, 1, 2, 7, 5, 4, 6, 3, 9, 8],
[0, 4, 3, 8, 5, 1, 9, 2, 6, 7],
[1, 2, 3, 8, 6, 0, 7, 4, 5, 9],
],
)
def suite():
isomorphism_suite = unittest.defaultTestLoader.loadTestsFromTestCase(
IsomorphismTests
)
subisomorphism_suite = unittest.defaultTestLoader.loadTestsFromTestCase(
SubisomorphismTests
)
permutation_suite = unittest.defaultTestLoader.loadTestsFromTestCase(
PermutationTests
)
automorphism_suite = unittest.defaultTestLoader.loadTestsFromTestCase(
AutomorphismTests
)
return unittest.TestSuite(
[
isomorphism_suite,
subisomorphism_suite,
permutation_suite,
automorphism_suite,
]
)
def test():
runner = unittest.TextTestRunner()
runner.run(suite())
if __name__ == "__main__":
test()
|
