FindVertexIndependentPaths

FindVertexIndependentPaths[g,s,t,k]

finds at most k vertex-independent paths from vertex s to vertex t in the graph g.

FindVertexIndependentPaths[{vw,},]

uses rules vw to specify the graph g.

Details

• Vertex-independent paths are also known as independent paths or vertex disjoint paths.
• FindVertexIndependentPaths returns a list of vertex-independent paths from s to t.
• Each path is given as a list of vertices.
• FindVertexIndependentPaths works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

Examples

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Basic Examples(1)

Find a vertex-independent path between two individual vertices in a graph:

Show the path:

Scope(6)

FindVertexIndependentPaths works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

FindVertexIndependentPaths works with large graphs:

Properties & Relations(2)

FindVertexIndependentPaths only returns simple paths:

VertexConnectivity gives the maximum number of vertex-independent paths:

Possible Issues(1)

Find a largest set of vertex-independent paths between two vertices:

Another vertex-independent path:

Wolfram Research (2014), FindVertexIndependentPaths, Wolfram Language function, https://reference.wolfram.com/language/ref/FindVertexIndependentPaths.html (updated 2015).

Text

Wolfram Research (2014), FindVertexIndependentPaths, Wolfram Language function, https://reference.wolfram.com/language/ref/FindVertexIndependentPaths.html (updated 2015).

CMS

Wolfram Language. 2014. "FindVertexIndependentPaths." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/FindVertexIndependentPaths.html.

APA

Wolfram Language. (2014). FindVertexIndependentPaths. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindVertexIndependentPaths.html

BibTeX

@misc{reference.wolfram_2024_findvertexindependentpaths, author="Wolfram Research", title="{FindVertexIndependentPaths}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/FindVertexIndependentPaths.html}", note=[Accessed: 17-July-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_findvertexindependentpaths, organization={Wolfram Research}, title={FindVertexIndependentPaths}, year={2015}, url={https://reference.wolfram.com/language/ref/FindVertexIndependentPaths.html}, note=[Accessed: 17-July-2024 ]}