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

The girth of a graph is the length of the shortest cycle. This routine returns the girth (or infinity if the graph G has no cycle).

If a name such as shortcycle is specified, then this name is assigned the set of edges forming that shortest cycle.

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

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

$G≔\mathrm{cycle}\left(6\right)\:$

$\mathrm{girth}\left(G\,\mathrm{scyc}\right)$

$6$

$\mathrm{scyc}$

$\mathrm{e1},\mathrm{e2},\mathrm{e3},\mathrm{e4},\mathrm{e5},\mathrm{e6}$

$\mathrm{ends}\left(\left[\mathrm{scyc}\right]\,G\right)$

$\left[\left\{1\,2\right\}\,\left\{2\,3\right\}\,\left\{3\,4\right\}\,\left\{4\,5\right\}\,\left\{5\,6\right\}\,\left\{1\,6\right\}\right]$

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

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

$\mathrm{\infty }$

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

$\mathrm{girth}\left(G\,\mathrm{short}\right)$

$1$

$\mathrm{ends}\left(\mathrm{short}\,G\right)$

$\left\{1\right\}$