EdgeConnectivity

EdgeConnectivity[g]

gives the edge connectivity of the graph g.

EdgeConnectivity[g,s,t]

gives the s-t edge connectivity of the graph g.

EdgeConnectivity[{vw,…},…]

uses rules vw to specify the graph g.

Details and Options

  • EdgeConnectivity is also known as line connectivity.
  • The edge connectivity of a graph g is the smallest number of edges whose deletion from g disconnects g.
  • The s-t edge connectivity is the smallest number of edges whose deletion from g disconnects g, with s and t in two different connected components.
  • For weighted graphs, EdgeConnectivity gives the smallest sum of edge weights.
  • For a disconnected graph, EdgeConnectivity will return 0.
  • The following option can be given:
  • EdgeWeight Automaticedge weight for each edge

Examples

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Basic Examples  (2)

Find the edge connectivity:

Find the edge connectivity between two vertices:

Scope  (7)

EdgeConnectivity works on undirected graphs:

Directed graphs:

Weighted graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

EdgeConnectivity works on large graphs:

Options  (1)

EdgeWeight  (1)

By default, the edge weight of an edge is taken to be its EdgeWeight property if available, otherwise 1:

Use EdgeWeight->weights to set the edge weight:

Properties & Relations  (3)

Use FindEdgeCut to compute the edge connectivity:

The maximum flow between two vertices is equal to the edge connectivity:

EdgeConnectivity returns 0 for a disconnected graph:

Wolfram Research (2012), EdgeConnectivity, Wolfram Language function, https://reference.wolfram.com/language/ref/EdgeConnectivity.html (updated 2015).

Text

Wolfram Research (2012), EdgeConnectivity, Wolfram Language function, https://reference.wolfram.com/language/ref/EdgeConnectivity.html (updated 2015).

CMS

Wolfram Language. 2012. "EdgeConnectivity." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/EdgeConnectivity.html.

APA

Wolfram Language. (2012). EdgeConnectivity. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EdgeConnectivity.html

BibTeX

@misc{reference.wolfram_2024_edgeconnectivity, author="Wolfram Research", title="{EdgeConnectivity}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/EdgeConnectivity.html}", note=[Accessed: 21-November-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_edgeconnectivity, organization={Wolfram Research}, title={EdgeConnectivity}, year={2015}, url={https://reference.wolfram.com/language/ref/EdgeConnectivity.html}, note=[Accessed: 21-November-2024 ]}