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
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
|
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.19: https://docutils.sourceforge.io/" />
<title>node_disjoint_paths — NetworkX 3.0rc2.dev0 documentation</title>
<script data-cfasync="false">
document.documentElement.dataset.mode = localStorage.getItem("mode") || "light";
document.documentElement.dataset.theme = localStorage.getItem("theme") || "light";
</script>
<!-- Loaded before other Sphinx assets -->
<link href="../../../_static/styles/theme.css?digest=796348d33e8b1d947c94" rel="stylesheet">
<link href="../../../_static/styles/bootstrap.css?digest=796348d33e8b1d947c94" rel="stylesheet">
<link href="../../../_static/styles/pydata-sphinx-theme.css?digest=796348d33e8b1d947c94" rel="stylesheet">
<link href="../../../_static/vendor/fontawesome/6.1.2/css/all.min.css?digest=796348d33e8b1d947c94" rel="stylesheet">
<link rel="preload" as="font" type="font/woff2" crossorigin href="../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-solid-900.woff2">
<link rel="preload" as="font" type="font/woff2" crossorigin href="../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2">
<link rel="preload" as="font" type="font/woff2" crossorigin href="../../../_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2">
<link rel="stylesheet" type="text/css" href="../../../_static/pygments.css" />
<link rel="stylesheet" type="text/css" href="../../../_static/custom.css" />
<link rel="stylesheet" type="text/css" href="../../../_static/sg_gallery.css" />
<link rel="stylesheet" type="text/css" href="../../../_static/sg_gallery-binder.css" />
<link rel="stylesheet" type="text/css" href="../../../_static/sg_gallery-dataframe.css" />
<link rel="stylesheet" type="text/css" href="../../../_static/sg_gallery-rendered-html.css" />
<!-- Pre-loaded scripts that we'll load fully later -->
<link rel="preload" as="script" href="../../../_static/scripts/bootstrap.js?digest=796348d33e8b1d947c94">
<link rel="preload" as="script" href="../../../_static/scripts/pydata-sphinx-theme.js?digest=796348d33e8b1d947c94">
<script data-url_root="../../../" id="documentation_options" src="../../../_static/documentation_options.js"></script>
<script src="../../../_static/jquery.js"></script>
<script src="../../../_static/underscore.js"></script>
<script src="../../../_static/_sphinx_javascript_frameworks_compat.js"></script>
<script src="../../../_static/doctools.js"></script>
<script src="../../../_static/sphinx_highlight.js"></script>
<script src="../../../_static/copybutton.js"></script>
<script>DOCUMENTATION_OPTIONS.pagename = 'reference/algorithms/generated/networkx.algorithms.connectivity.disjoint_paths.node_disjoint_paths';</script>
<link rel="canonical" href="https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.connectivity.disjoint_paths.node_disjoint_paths.html" />
<link rel="search" type="application/opensearchdescription+xml"
title="Search within NetworkX 3.0rc2.dev0 documentation"
href="../../../_static/opensearch.xml"/>
<link rel="index" title="Index" href="../../../genindex.html" />
<link rel="search" title="Search" href="../../../search.html" />
<link rel="next" title="average_node_connectivity" href="networkx.algorithms.connectivity.connectivity.average_node_connectivity.html" />
<link rel="prev" title="edge_disjoint_paths" href="networkx.algorithms.connectivity.disjoint_paths.edge_disjoint_paths.html" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<meta name="docsearch:language" content="en">
</head>
<body data-spy="scroll" data-target="#bd-toc-nav" data-offset="180" data-default-mode="light">
<a class="skip-link" href="#main-content">Skip to main content</a>
<div class="container-fluid version-alert devbar">
<div class="row no-gutters">
<div class="col-12 text-center">
This page is documentation for a DEVELOPMENT / PRE-RELEASE version.
<a
class="btn version-stable font-weight-bold ml-3 my-3 align-baseline"
href="https://networkx.org/documentation/stable/"
>Switch to stable version</a
>
</div>
</div>
</div>
<input type="checkbox" class="sidebar-toggle" name="__primary" id="__primary">
<label class="overlay overlay-primary" for="__primary"></label>
<input type="checkbox" class="sidebar-toggle" name="__secondary" id="__secondary">
<label class="overlay overlay-secondary" for="__secondary"></label>
<div class="search-button__wrapper">
<div class="search-button__overlay"></div>
<div class="search-button__search-container">
<form class="bd-search d-flex align-items-center" action="../../../search.html" method="get">
<i class="fa-solid fa-magnifying-glass"></i>
<input type="search" class="form-control" name="q" id="search-input" placeholder="Search the docs ..." aria-label="Search the docs ..." autocomplete="off" autocorrect="off" autocapitalize="off" spellcheck="false">
<span class="search-button__kbd-shortcut"><kbd class="kbd-shortcut__modifier">Ctrl</kbd>+<kbd>K</kbd></span>
</form>
</div>
</div>
<nav class="bd-header navbar navbar-expand-lg bd-navbar" id="navbar-main"><div class="bd-header__inner bd-page-width">
<label class="sidebar-toggle primary-toggle" for="__primary">
<span class="fa-solid fa-bars"></span>
</label>
<div id="navbar-start">
<a class="navbar-brand logo" href="../../../index.html">
<img src="../../../_static/networkx_banner.svg" class="logo__image only-light" alt="Logo image">
<img src="../../../_static/networkx_banner.svg" class="logo__image only-dark" alt="Logo image">
</a>
</div>
<div class="col-lg-9 navbar-header-items">
<div id="navbar-center" class="mr-auto">
<div class="navbar-center-item">
<nav class="navbar-nav">
<p class="sidebar-header-items__title" role="heading" aria-level="1" aria-label="Site Navigation">
Site Navigation
</p>
<ul id="navbar-main-elements" class="navbar-nav">
<li class="nav-item">
<a class="nav-link nav-internal" href="../../../install.html">
Install
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../../../tutorial.html">
Tutorial
</a>
</li>
<li class="nav-item current active">
<a class="nav-link nav-internal" href="../../index.html">
Reference
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../../../auto_examples/index.html">
Gallery
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../../../developer/index.html">
Developer
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../../../release/index.html">
Releases
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-external" href="https://networkx.org/nx-guides/">
Guides
</a>
</li>
</ul>
</nav>
</div>
</div>
<div id="navbar-end">
<div class="navbar-end-item navbar-persistent--container">
<button class="btn btn-sm navbar-btn search-button search-button__button" title="Search" aria-label="Search" data-toggle="tooltip">
<i class="fa-solid fa-magnifying-glass"></i>
</button>
</div>
<div class="navbar-end-item">
<button class="theme-switch-button btn btn-sm btn-outline-primary navbar-btn rounded-circle" title="light/dark" aria-label="light/dark" data-toggle="tooltip">
<span class="theme-switch" data-mode="light"><i class="fa-solid fa-sun"></i></span>
<span class="theme-switch" data-mode="dark"><i class="fa-solid fa-moon"></i></span>
<span class="theme-switch" data-mode="auto"><i class="fa-solid fa-circle-half-stroke"></i></span>
</button>
</div>
<div class="navbar-end-item">
<ul id="navbar-icon-links" class="navbar-nav" aria-label="Icon Links">
<li class="nav-item">
<a href="https://networkx.org" title="Home Page" class="nav-link" rel="noopener" target="_blank" data-toggle="tooltip"><span><i class="fas fa-home"></i></span>
<label class="sr-only">Home Page</label></a>
</li>
<li class="nav-item">
<a href="https://github.com/networkx/networkx" title="GitHub" class="nav-link" rel="noopener" target="_blank" data-toggle="tooltip"><span><i class="fab fa-github-square"></i></span>
<label class="sr-only">GitHub</label></a>
</li>
</ul>
</div>
<div class="navbar-end-item">
<ul class="navbar-nav">
<li class="mr-2 dropdown">
<button
type="button"
class="btn btn-version btn-sm navbar-btn dropdown-toggle"
id="dLabelMore"
data-toggle="dropdown"
>
v3.0rc2.dev0
<span class="caret"></span>
</button>
<ul class="dropdown-menu" aria-labelledby="dLabelMore">
<li>
<a href="https://networkx.org/documentation/latest/index.html"
>devel (latest)</a
>
</li>
<li>
<a href="https://networkx.org/documentation/stable/index.html"
>current (stable)</a
>
</li>
</ul>
</li>
</ul>
</div>
</div>
</div>
<div class="navbar-persistent--mobile">
<button class="btn btn-sm navbar-btn search-button search-button__button" title="Search" aria-label="Search" data-toggle="tooltip">
<i class="fa-solid fa-magnifying-glass"></i>
</button>
</div>
<label class="sidebar-toggle secondary-toggle" for="__secondary">
<span class="fa-solid fa-outdent"></span>
</label>
</div>
</nav>
<div class="bd-container">
<div class="bd-container__inner bd-page-width">
<div class="bd-sidebar-primary bd-sidebar">
<div class="sidebar-header-items sidebar-primary__section">
<div class="sidebar-header-items__center">
<div class="navbar-center-item">
<nav class="navbar-nav">
<p class="sidebar-header-items__title" role="heading" aria-level="1" aria-label="Site Navigation">
Site Navigation
</p>
<ul id="navbar-main-elements" class="navbar-nav">
<li class="nav-item">
<a class="nav-link nav-internal" href="../../../install.html">
Install
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../../../tutorial.html">
Tutorial
</a>
</li>
<li class="nav-item current active">
<a class="nav-link nav-internal" href="../../index.html">
Reference
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../../../auto_examples/index.html">
Gallery
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../../../developer/index.html">
Developer
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-internal" href="../../../release/index.html">
Releases
</a>
</li>
<li class="nav-item">
<a class="nav-link nav-external" href="https://networkx.org/nx-guides/">
Guides
</a>
</li>
</ul>
</nav>
</div>
</div>
<div class="sidebar-header-items__end">
<div class="navbar-end-item">
<button class="theme-switch-button btn btn-sm btn-outline-primary navbar-btn rounded-circle" title="light/dark" aria-label="light/dark" data-toggle="tooltip">
<span class="theme-switch" data-mode="light"><i class="fa-solid fa-sun"></i></span>
<span class="theme-switch" data-mode="dark"><i class="fa-solid fa-moon"></i></span>
<span class="theme-switch" data-mode="auto"><i class="fa-solid fa-circle-half-stroke"></i></span>
</button>
</div>
<div class="navbar-end-item">
<ul id="navbar-icon-links" class="navbar-nav" aria-label="Icon Links">
<li class="nav-item">
<a href="https://networkx.org" title="Home Page" class="nav-link" rel="noopener" target="_blank" data-toggle="tooltip"><span><i class="fas fa-home"></i></span>
<label class="sr-only">Home Page</label></a>
</li>
<li class="nav-item">
<a href="https://github.com/networkx/networkx" title="GitHub" class="nav-link" rel="noopener" target="_blank" data-toggle="tooltip"><span><i class="fab fa-github-square"></i></span>
<label class="sr-only">GitHub</label></a>
</li>
</ul>
</div>
<div class="navbar-end-item">
<ul class="navbar-nav">
<li class="mr-2 dropdown">
<button
type="button"
class="btn btn-version btn-sm navbar-btn dropdown-toggle"
id="dLabelMore"
data-toggle="dropdown"
>
v3.0rc2.dev0
<span class="caret"></span>
</button>
<ul class="dropdown-menu" aria-labelledby="dLabelMore">
<li>
<a href="https://networkx.org/documentation/latest/index.html"
>devel (latest)</a
>
</li>
<li>
<a href="https://networkx.org/documentation/stable/index.html"
>current (stable)</a
>
</li>
</ul>
</li>
</ul>
</div>
</div>
</div>
<div class="sidebar-start-items sidebar-primary__section">
<div class="sidebar-start-items__item"><nav class="bd-links" id="bd-docs-nav" aria-label="Section navigation">
<p class="bd-links__title" role="heading" aria-level="1">
Section Navigation
</p>
<div class="bd-toc-item navbar-nav">
<ul class="current nav bd-sidenav">
<li class="toctree-l1"><a class="reference internal" href="../../introduction.html">Introduction</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../classes/index.html">Graph types</a></li>
<li class="toctree-l1 current active has-children"><a class="reference internal" href="../index.html">Algorithms</a><input checked="" class="toctree-checkbox" id="toctree-checkbox-1" name="toctree-checkbox-1" type="checkbox"/><label class="toctree-toggle" for="toctree-checkbox-1"><i class="fa-solid fa-chevron-down"></i></label><ul class="current">
<li class="toctree-l2"><a class="reference internal" href="../approximation.html">Approximations and Heuristics</a></li>
<li class="toctree-l2"><a class="reference internal" href="../assortativity.html">Assortativity</a></li>
<li class="toctree-l2"><a class="reference internal" href="../asteroidal.html">Asteroidal</a></li>
<li class="toctree-l2"><a class="reference internal" href="../bipartite.html">Bipartite</a></li>
<li class="toctree-l2"><a class="reference internal" href="../boundary.html">Boundary</a></li>
<li class="toctree-l2"><a class="reference internal" href="../bridges.html">Bridges</a></li>
<li class="toctree-l2"><a class="reference internal" href="../centrality.html">Centrality</a></li>
<li class="toctree-l2"><a class="reference internal" href="../chains.html">Chains</a></li>
<li class="toctree-l2"><a class="reference internal" href="../chordal.html">Chordal</a></li>
<li class="toctree-l2"><a class="reference internal" href="../clique.html">Clique</a></li>
<li class="toctree-l2"><a class="reference internal" href="../clustering.html">Clustering</a></li>
<li class="toctree-l2"><a class="reference internal" href="../coloring.html">Coloring</a></li>
<li class="toctree-l2"><a class="reference internal" href="../communicability_alg.html">Communicability</a></li>
<li class="toctree-l2"><a class="reference internal" href="../community.html">Communities</a></li>
<li class="toctree-l2"><a class="reference internal" href="../component.html">Components</a></li>
<li class="toctree-l2 current active"><a class="reference internal" href="../connectivity.html">Connectivity</a></li>
<li class="toctree-l2"><a class="reference internal" href="../core.html">Cores</a></li>
<li class="toctree-l2"><a class="reference internal" href="../covering.html">Covering</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cycles.html">Cycles</a></li>
<li class="toctree-l2"><a class="reference internal" href="../cuts.html">Cuts</a></li>
<li class="toctree-l2"><a class="reference internal" href="../d_separation.html">D-Separation</a></li>
<li class="toctree-l2"><a class="reference internal" href="../dag.html">Directed Acyclic Graphs</a></li>
<li class="toctree-l2"><a class="reference internal" href="../distance_measures.html">Distance Measures</a></li>
<li class="toctree-l2"><a class="reference internal" href="../distance_regular.html">Distance-Regular Graphs</a></li>
<li class="toctree-l2"><a class="reference internal" href="../dominance.html">Dominance</a></li>
<li class="toctree-l2"><a class="reference internal" href="../dominating.html">Dominating Sets</a></li>
<li class="toctree-l2"><a class="reference internal" href="../efficiency_measures.html">Efficiency</a></li>
<li class="toctree-l2"><a class="reference internal" href="../euler.html">Eulerian</a></li>
<li class="toctree-l2"><a class="reference internal" href="../flow.html">Flows</a></li>
<li class="toctree-l2"><a class="reference internal" href="../graph_hashing.html">Graph Hashing</a></li>
<li class="toctree-l2"><a class="reference internal" href="../graphical.html">Graphical degree sequence</a></li>
<li class="toctree-l2"><a class="reference internal" href="../hierarchy.html">Hierarchy</a></li>
<li class="toctree-l2"><a class="reference internal" href="../hybrid.html">Hybrid</a></li>
<li class="toctree-l2"><a class="reference internal" href="../isolates.html">Isolates</a></li>
<li class="toctree-l2"><a class="reference internal" href="../isomorphism.html">Isomorphism</a></li>
<li class="toctree-l2"><a class="reference internal" href="../link_analysis.html">Link Analysis</a></li>
<li class="toctree-l2"><a class="reference internal" href="../link_prediction.html">Link Prediction</a></li>
<li class="toctree-l2"><a class="reference internal" href="../lowest_common_ancestors.html">Lowest Common Ancestor</a></li>
<li class="toctree-l2"><a class="reference internal" href="../matching.html">Matching</a></li>
<li class="toctree-l2"><a class="reference internal" href="../minors.html">Minors</a></li>
<li class="toctree-l2"><a class="reference internal" href="../mis.html">Maximal independent set</a></li>
<li class="toctree-l2"><a class="reference internal" href="../non_randomness.html">non-randomness</a></li>
<li class="toctree-l2"><a class="reference internal" href="../moral.html">Moral</a></li>
<li class="toctree-l2"><a class="reference internal" href="../node_classification.html">Node Classification</a></li>
<li class="toctree-l2"><a class="reference internal" href="../operators.html">Operators</a></li>
<li class="toctree-l2"><a class="reference internal" href="../planarity.html">Planarity</a></li>
<li class="toctree-l2"><a class="reference internal" href="../planar_drawing.html">Planar Drawing</a></li>
<li class="toctree-l2"><a class="reference internal" href="../polynomials.html">Graph Polynomials</a></li>
<li class="toctree-l2"><a class="reference internal" href="../reciprocity.html">Reciprocity</a></li>
<li class="toctree-l2"><a class="reference internal" href="../regular.html">Regular</a></li>
<li class="toctree-l2"><a class="reference internal" href="../rich_club.html">Rich Club</a></li>
<li class="toctree-l2"><a class="reference internal" href="../shortest_paths.html">Shortest Paths</a></li>
<li class="toctree-l2"><a class="reference internal" href="../similarity.html">Similarity Measures</a></li>
<li class="toctree-l2"><a class="reference internal" href="../simple_paths.html">Simple Paths</a></li>
<li class="toctree-l2"><a class="reference internal" href="../smallworld.html">Small-world</a></li>
<li class="toctree-l2"><a class="reference internal" href="../smetric.html">s metric</a></li>
<li class="toctree-l2"><a class="reference internal" href="../sparsifiers.html">Sparsifiers</a></li>
<li class="toctree-l2"><a class="reference internal" href="../structuralholes.html">Structural holes</a></li>
<li class="toctree-l2"><a class="reference internal" href="../summarization.html">Summarization</a></li>
<li class="toctree-l2"><a class="reference internal" href="../swap.html">Swap</a></li>
<li class="toctree-l2"><a class="reference internal" href="../threshold.html">Threshold Graphs</a></li>
<li class="toctree-l2"><a class="reference internal" href="../tournament.html">Tournament</a></li>
<li class="toctree-l2"><a class="reference internal" href="../traversal.html">Traversal</a></li>
<li class="toctree-l2"><a class="reference internal" href="../tree.html">Tree</a></li>
<li class="toctree-l2"><a class="reference internal" href="../triads.html">Triads</a></li>
<li class="toctree-l2"><a class="reference internal" href="../vitality.html">Vitality</a></li>
<li class="toctree-l2"><a class="reference internal" href="../voronoi.html">Voronoi cells</a></li>
<li class="toctree-l2"><a class="reference internal" href="../wiener.html">Wiener index</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="../../functions.html">Functions</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../generators.html">Graph generators</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../linalg.html">Linear algebra</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../convert.html">Converting to and from other data formats</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../relabel.html">Relabeling nodes</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../readwrite/index.html">Reading and writing graphs</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../drawing.html">Drawing</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../randomness.html">Randomness</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../exceptions.html">Exceptions</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../utils.html">Utilities</a></li>
<li class="toctree-l1"><a class="reference internal" href="../../glossary.html">Glossary</a></li>
</ul>
</div>
</nav>
</div>
<div class="sidebar-start-items__item">
</div>
</div>
<div class="sidebar-end-items sidebar-primary__section">
<div class="sidebar-end-items__item">
</div>
</div>
<div id="rtd-footer-container"></div>
</div>
<main id="main-content" class="bd-main">
<div class="bd-content">
<div class="bd-article-container">
<div class="bd-header-article">
</div>
<article class="bd-article" role="main">
<section id="node-disjoint-paths">
<h1>node_disjoint_paths<a class="headerlink" href="#node-disjoint-paths" title="Permalink to this heading">#</a></h1>
<dl class="py function">
<dt class="sig sig-object py" id="networkx.algorithms.connectivity.disjoint_paths.node_disjoint_paths">
<span class="sig-name descname"><span class="pre">node_disjoint_paths</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">G</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">s</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">t</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">flow_func</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cutoff</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">auxiliary</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">residual</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../../_modules/networkx/algorithms/connectivity/disjoint_paths.html#node_disjoint_paths"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#networkx.algorithms.connectivity.disjoint_paths.node_disjoint_paths" title="Permalink to this definition">#</a></dt>
<dd><p>Computes node disjoint paths between source and target.</p>
<p>Node disjoint paths are paths that only share their first and last
nodes. The number of node independent paths between two nodes is
equal to their local node connectivity.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>G</strong><span class="classifier">NetworkX graph</span></dt><dd></dd>
<dt><strong>s</strong><span class="classifier">node</span></dt><dd><p>Source node.</p>
</dd>
<dt><strong>t</strong><span class="classifier">node</span></dt><dd><p>Target node.</p>
</dd>
<dt><strong>flow_func</strong><span class="classifier">function</span></dt><dd><p>A function for computing the maximum flow among a pair of nodes.
The function has to accept at least three parameters: a Digraph,
a source node, and a target node. And return a residual network
that follows NetworkX conventions (see <code class="xref py py-meth docutils literal notranslate"><span class="pre">maximum_flow()</span></code> for
details). If flow_func is None, the default maximum flow function
(<code class="xref py py-meth docutils literal notranslate"><span class="pre">edmonds_karp()</span></code>) is used. See below for details. The choice
of the default function may change from version to version and
should not be relied on. Default value: None.</p>
</dd>
<dt><strong>cutoff</strong><span class="classifier">integer or None (default: None)</span></dt><dd><p>Maximum number of paths to yield. If specified, the maximum flow
algorithm will terminate when the flow value reaches or exceeds the
cutoff. This only works for flows that support the cutoff parameter
(most do) and is ignored otherwise.</p>
</dd>
<dt><strong>auxiliary</strong><span class="classifier">NetworkX DiGraph</span></dt><dd><p>Auxiliary digraph to compute flow based node connectivity. It has
to have a graph attribute called mapping with a dictionary mapping
node names in G and in the auxiliary digraph. If provided
it will be reused instead of recreated. Default value: None.</p>
</dd>
<dt><strong>residual</strong><span class="classifier">NetworkX DiGraph</span></dt><dd><p>Residual network to compute maximum flow. If provided it will be
reused instead of recreated. Default value: None.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><dl class="simple">
<dt><strong>paths</strong><span class="classifier">generator</span></dt><dd><p>Generator of node disjoint paths.</p>
</dd>
</dl>
</dd>
<dt class="field-odd">Raises<span class="colon">:</span></dt>
<dd class="field-odd"><dl class="simple">
<dt>NetworkXNoPath</dt><dd><p>If there is no path between source and target.</p>
</dd>
<dt>NetworkXError</dt><dd><p>If source or target are not in the graph G.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="networkx.algorithms.connectivity.disjoint_paths.edge_disjoint_paths.html#networkx.algorithms.connectivity.disjoint_paths.edge_disjoint_paths" title="networkx.algorithms.connectivity.disjoint_paths.edge_disjoint_paths"><code class="xref py py-meth docutils literal notranslate"><span class="pre">edge_disjoint_paths()</span></code></a></dt><dd></dd>
<dt><code class="xref py py-meth docutils literal notranslate"><span class="pre">node_connectivity()</span></code></dt><dd></dd>
<dt><code class="xref py py-meth docutils literal notranslate"><span class="pre">maximum_flow()</span></code></dt><dd></dd>
<dt><code class="xref py py-meth docutils literal notranslate"><span class="pre">edmonds_karp()</span></code></dt><dd></dd>
<dt><code class="xref py py-meth docutils literal notranslate"><span class="pre">preflow_push()</span></code></dt><dd></dd>
<dt><code class="xref py py-meth docutils literal notranslate"><span class="pre">shortest_augmenting_path()</span></code></dt><dd></dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>This is a flow based implementation of node disjoint paths. We compute
the maximum flow between source and target on an auxiliary directed
network. The saturated edges in the residual network after running the
maximum flow algorithm correspond to node disjoint paths between source
and target in the original network. This function handles both directed
and undirected graphs, and can use all flow algorithms from NetworkX flow
package.</p>
<p class="rubric">Examples</p>
<p>We use in this example the platonic icosahedral graph, which has node
connectivity 5, thus there are 5 node disjoint paths between any pair
of non neighbor nodes.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">G</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">icosahedral_graph</span><span class="p">()</span>
<span class="gp">>>> </span><span class="nb">len</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">nx</span><span class="o">.</span><span class="n">node_disjoint_paths</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">6</span><span class="p">)))</span>
<span class="go">5</span>
</pre></div>
</div>
<p>If you need to compute node disjoint paths between several pairs of
nodes in the same graph, it is recommended that you reuse the
data structures that NetworkX uses in the computation: the
auxiliary digraph for node connectivity and node cuts, and the
residual network for the underlying maximum flow computation.</p>
<p>Example of how to compute node disjoint paths reusing the data
structures:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="c1"># You also have to explicitly import the function for</span>
<span class="gp">>>> </span><span class="c1"># building the auxiliary digraph from the connectivity package</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">networkx.algorithms.connectivity</span> <span class="kn">import</span> <span class="n">build_auxiliary_node_connectivity</span>
<span class="gp">>>> </span><span class="n">H</span> <span class="o">=</span> <span class="n">build_auxiliary_node_connectivity</span><span class="p">(</span><span class="n">G</span><span class="p">)</span>
<span class="gp">>>> </span><span class="c1"># And the function for building the residual network from the</span>
<span class="gp">>>> </span><span class="c1"># flow package</span>
<span class="gp">>>> </span><span class="kn">from</span> <span class="nn">networkx.algorithms.flow</span> <span class="kn">import</span> <span class="n">build_residual_network</span>
<span class="gp">>>> </span><span class="c1"># Note that the auxiliary digraph has an edge attribute named capacity</span>
<span class="gp">>>> </span><span class="n">R</span> <span class="o">=</span> <span class="n">build_residual_network</span><span class="p">(</span><span class="n">H</span><span class="p">,</span> <span class="s2">"capacity"</span><span class="p">)</span>
<span class="gp">>>> </span><span class="c1"># Reuse the auxiliary digraph and the residual network by passing them</span>
<span class="gp">>>> </span><span class="c1"># as arguments</span>
<span class="gp">>>> </span><span class="nb">len</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">nx</span><span class="o">.</span><span class="n">node_disjoint_paths</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="n">auxiliary</span><span class="o">=</span><span class="n">H</span><span class="p">,</span> <span class="n">residual</span><span class="o">=</span><span class="n">R</span><span class="p">)))</span>
<span class="go">5</span>
</pre></div>
</div>
<p>You can also use alternative flow algorithms for computing node disjoint
paths. For instance, in dense networks the algorithm
<code class="xref py py-meth docutils literal notranslate"><span class="pre">shortest_augmenting_path()</span></code> will usually perform better than
the default <code class="xref py py-meth docutils literal notranslate"><span class="pre">edmonds_karp()</span></code> which is faster for sparse
networks with highly skewed degree distributions. Alternative flow
functions have to be explicitly imported from the flow package.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span> <span class="nn">networkx.algorithms.flow</span> <span class="kn">import</span> <span class="n">shortest_augmenting_path</span>
<span class="gp">>>> </span><span class="nb">len</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">nx</span><span class="o">.</span><span class="n">node_disjoint_paths</span><span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="n">flow_func</span><span class="o">=</span><span class="n">shortest_augmenting_path</span><span class="p">)))</span>
<span class="go">5</span>
</pre></div>
</div>
</dd></dl>
</section>
</article>
</div>
<div class="bd-sidebar-secondary bd-toc">
<div class="toc-item">
<div class="tocsection onthispage">
<i class="fa-solid fa-list"></i> On this page
</div>
<nav id="bd-toc-nav" class="page-toc">
<ul class="visible nav section-nav flex-column">
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#networkx.algorithms.connectivity.disjoint_paths.node_disjoint_paths">
<code class="docutils literal notranslate">
<span class="pre">
node_disjoint_paths()
</span>
</code>
</a>
</li>
</ul>
</nav>
</div>
<div class="toc-item">
<div id="searchbox"></div>
</div>
<div class="toc-item">
</div>
<div class="toc-item">
</div>
</div>
</div>
<footer class="bd-footer-content">
<div class="bd-footer-content__inner">
</div>
</footer>
</main>
</div>
</div>
<!-- Scripts loaded after <body> so the DOM is not blocked -->
<script src="../../../_static/scripts/bootstrap.js?digest=796348d33e8b1d947c94"></script>
<script src="../../../_static/scripts/pydata-sphinx-theme.js?digest=796348d33e8b1d947c94"></script>
<footer class="bd-footer"><div class="bd-footer__inner container">
<div class="footer-item">
<p class="copyright">
© Copyright 2004-2022, NetworkX Developers.<br>
</p>
</div>
<div class="footer-item">
<p class="theme-version">
Built with the
<a href="https://pydata-sphinx-theme.readthedocs.io/en/stable/index.html">
PyData Sphinx Theme
</a>
0.12.0.
</p>
</div>
<div class="footer-item">
<p class="sphinx-version">
Created using <a href="http://sphinx-doc.org/">Sphinx</a> 5.2.3.<br>
</p>
</div>
</div>
</footer>
</body>
</html>
|
