Important: The networks package has been deprecated.  Use the superseding command GraphTheory[BiconnectedComponents] instead.

A connected graph can be decomposed into two connected components possibly connected by bridges. This routine returns two sets in a list of length 2:  the first indicating the bridges and the second indicating the biconnected components.

Bridges are specified as edges.  The set of bridges may be empty.

The biconnected components are each specified as sets of edges. This set of bicomponents may be empty as for example in the case of a path.

This routine is normally loaded using the command with(networks) but may also be referenced using the full name networks[bicomponents](...).

$\mathrm{with}\left(\mathrm{networks}\right)\:$

$G≔\mathrm{cycle}\left(5\right)\:$

$\mathrm{bicomponents}\left(G\right)$

$\left[\varnothing \,\left\{\left\{\mathrm{e1}\,\mathrm{e2}\,\mathrm{e3}\,\mathrm{e4}\,\mathrm{e5}\right\}\right\}\right]$

$\mathrm{delete}\left(\mathrm{e1}\,G\right)\:$

$\mathrm{bicomponents}\left(G\right)$

$\left[\left\{\mathrm{e2}\,\mathrm{e3}\,\mathrm{e4}\,\mathrm{e5}\right\}\,\varnothing \right]$

$\mathrm{addedge}\left(\mathrm{Cycle}\left(1\,2\,3\right)\,G\right)\:$

$\mathrm{addedge}\left(\mathrm{Cycle}\left(3\,4\,5\right)\,G\right)\:$

$\mathrm{bicomponents}\left(G\right)$

$\left[\varnothing \,\left\{\left\{\mathrm{e10}\,\mathrm{e11}\,\mathrm{e2}\,\mathrm{e3}\,\mathrm{e4}\,\mathrm{e5}\,\mathrm{e6}\,\mathrm{e7}\,\mathrm{e8}\,\mathrm{e9}\right\}\right\}\right]$