networks(deprecated)/cyclebase - Help

networks

 cyclebase
 finds a cycle basis in an undirected graph

 Calling Sequence cyclebase(G)

Parameters

 G - graph or network

Description

 • Important: The networks package has been deprecated.  Use the superseding command GraphTheory[CycleBasis] instead.
 • A spanning tree is found, and fundcyc() is then used to find all fundamental cycles with respect to this tree. They are returned as a set of cycles with each cycle being represented by a set of edges.
 • The subgraphs corresponding to these cycles can be constructed using induce().
 • This routine is normally loaded via the command with(networks) but may also be referenced using the full name networks[cyclebase](...).

Examples

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

 > $\mathrm{with}\left(\mathrm{networks}\right):$
 > $G≔\mathrm{complete}\left(4\right):$
 > $\mathrm{cyclebase}\left(G\right)$
 $\left\{\left\{{\mathrm{e1}}{,}{\mathrm{e3}}{,}{\mathrm{e5}}\right\}{,}\left\{{\mathrm{e2}}{,}{\mathrm{e3}}{,}{\mathrm{e6}}\right\}{,}\left\{{\mathrm{e1}}{,}{\mathrm{e3}}{,}{\mathrm{e4}}{,}{\mathrm{e6}}\right\}\right\}$ (1)