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

  • 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:
  • EdgeWeightAutomaticedge 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)