This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 GRAPH UTILITIES PACKAGE SYMBOL

# Bicomponents

 Bicomponents[g] gives the biconnected components of the undirected graph g.
• 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.
• treats the input g as an undirected graph.
This shows that a simple line with two vertices is biconnected:
This defines a small graph:
The graph has four bicomponents, one for each cycle and two for the line joining the cycles:
Needs["GraphUtilities`"]
This shows that a simple line with two vertices is biconnected:
 Out[3]=
 Out[4]=

Needs["GraphUtilities`"]
This defines a small graph:
 Out[3]=
The graph has four bicomponents, one for each cycle and two for the line joining the cycles:
 Out[4]=
This defines a graph:
This shows its biconnected components and connected components:
The result from WeakComponents is always smaller than that of :