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

Given a subset e of edges forming a unicyclic subgraph of a graph G, the edges forming the unique cycle are returned as a set.  It is assumed that only one cycle is present.

If no cycle exists then the empty set is returned.

When a spanning tree is known, fundcyc allows one to extract the fundamental cycles of a cycle basis by adding one edge at a time to the tree.

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

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

$G≔\mathrm{complete}\left(4\right)\:$

$\mathrm{sptree}≔\mathrm{edges}\left(\mathrm{spantree}\left(G\right)\right)$

$\mathrm{sptree}≔\left\{\mathrm{e1}\,\mathrm{e3}\,\mathrm{e6}\right\}$

$e≔\mathrm{op}\left(1\,\mathrm{edges}\left(G\right)\mathbf{minus}\mathrm{sptree}\right)$

$e≔\mathrm{e2}$

$\mathrm{fundcyc}\left(\mathrm{sptree}\mathbf{union}\left\{e\right\}\,G\right)$

$\left\{\mathrm{e2}\,\mathrm{e3}\,\mathrm{e6}\right\}$