networks(deprecated)/bicomponents - Help

networks

 bicomponents
 compute the biconnected components of a graph

 Calling Sequence bicomponents(G)

Parameters

 G - graph or network

Description

 • 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](...).

Examples

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

 > $\mathrm{with}\left(\mathrm{networks}\right):$
 > $G≔\mathrm{cycle}\left(5\right):$
 > $\mathrm{bicomponents}\left(G\right)$
 $\left[\left\{{}\right\}{,}\left\{\left\{{\mathrm{e1}}{,}{\mathrm{e2}}{,}{\mathrm{e3}}{,}{\mathrm{e4}}{,}{\mathrm{e5}}\right\}\right\}\right]$ (1)
 > $\mathrm{delete}\left(\mathrm{e1},G\right):$
 > $\mathrm{bicomponents}\left(G\right)$
 $\left[\left\{{\mathrm{e2}}{,}{\mathrm{e3}}{,}{\mathrm{e4}}{,}{\mathrm{e5}}\right\}{,}\left\{{}\right\}\right]$ (2)
 > $\mathrm{addedge}\left(\mathrm{Cycle}\left(1,2,3\right),G\right):$
 > $\mathrm{addedge}\left(\mathrm{Cycle}\left(3,4,5\right),G\right):$
 > $\mathrm{bicomponents}\left(G\right)$
 $\left[\left\{{}\right\}{,}\left\{\left\{{\mathrm{e10}}{,}{\mathrm{e11}}{,}{\mathrm{e2}}{,}{\mathrm{e3}}{,}{\mathrm{e4}}{,}{\mathrm{e5}}{,}{\mathrm{e6}}{,}{\mathrm{e7}}{,}{\mathrm{e8}}{,}{\mathrm{e9}}\right\}\right\}\right]$ (3)