GraphUtilities`

Bicomponents

As of Version 10, all the functionality of the GraphUtilities package is built into the Wolfram System. »

Bicomponents[g]

gives the biconnected components of the undirected graph g.

Details and Options

Bicomponents functionality is now available in the built-in Wolfram Language function KVertexConnectedComponents.
To use Bicomponents, you first need to load the Graph Utilities Package using Needs["GraphUtilities`"].
A biconnected component is a maximal subgraph that has no cutpoint, where a cutpoint is a vertex v such that the subgraph becomes disconnected if v and all its edges are removed.
Bicomponents treats the input g as an undirected graph.

open allclose all

This shows that a simple line with two vertices is biconnected:

Bicomponents has been superseded by KVertexConnectedComponents:

This defines a small graph:

The graph has four bicomponents, one for each cycle and two for the line joining the cycles:

This shows that a simple line with two vertices is biconnected:

This defines a graph:

This shows its biconnected components and connected components:

The result from WeakComponents is always smaller than that of Bicomponents:

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