# KEdgeConnectedComponents

gives the k-edge-connected components of the graph g.

KEdgeConnectedComponents[g,k,{v1,v2,}]

gives the k-edge-connected components that include at least one of the vertices v1, v2, .

KEdgeConnectedComponents[{vw,},]

uses rules vw to specify the graph g.

# Details • KEdgeConnectedComponents is also known as k-edge components.
• KEdgeConnectedComponents returns a list of components {c1,c2,}, where each component ci is given as a list of vertices.
• The component ci generates a maximal k-edge-connected subgraph of g.
• For an undirected graph, the vertices u and v are in the same component if there are at least k edge-disjoint paths from u to v.
• For a directed graph, the vertices u and v are in the same component if there are at least k edge-disjoint directed paths from u to v and from v to u.

# Examples

open allclose all

## Basic Examples(2)

Find 3-edge-connected components of a graph:

Show the 3-edge-connected components:

Find the 4-edge-connected components in a social network:

## Scope(8)

KEdgeConnectedComponents works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Select 3-edge-connected components that include at least one of the specified vertices:

Use rules to specify the graph:

Use patterns to select components:

Works with large graphs:

## Applications(1)

Highlight the k-edge-connected components of a graph:

## Properties & Relations(1)

A k-edge-connected graph has a k-edge-connected component as itself: