# FindEdgeIndependentPaths

FindEdgeIndependentPaths[g,s,t,k]

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

FindEdgeIndependentPaths[{vw,},]

uses rules vw to specify the graph g.

# Details

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

# Examples

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## Basic Examples(1)

Find edge-independent paths between two individual vertices in a graph:

Show the paths:

## Scope(6)

FindEdgeIndependentPaths works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

FindEdgeIndependentPaths works with large graphs:

## Properties & Relations(2)

FindEdgeIndependentPaths only returns simple paths:

EdgeConnectivity gives the maximum number of edge-independent paths:

## Possible Issues(1)

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

Another edge-independent path:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_findedgeindependentpaths, author="Wolfram Research", title="{FindEdgeIndependentPaths}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/FindEdgeIndependentPaths.html}", note=[Accessed: 19-May-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_findedgeindependentpaths, organization={Wolfram Research}, title={FindEdgeIndependentPaths}, year={2015}, url={https://reference.wolfram.com/language/ref/FindEdgeIndependentPaths.html}, note=[Accessed: 19-May-2024 ]}