# EdgeConnectivity

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 • 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 Automatic edge 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:

Introduced in 2012
(9.0)
|
Updated in 2015
(10.3)