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

The flow polynomial in variable h gives the number of nowhere-zero flows on G with edge labels chosen from integers modulo h.

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

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

$G≔\mathrm{complete}\left(4\right)\:$

$\mathrm{flowpoly}\left(G\,x\right)$

$x^3-6x^2+11x-6$

$\mathrm{addvertex}\left(5\,G\right)$

$5$

$\mathrm{addedge}\left(\left\{\left\{1\,2\right\}\,\left\{1\,5\right\}\right\}\,G\right)\:$

$\mathrm{flowpoly}\left(G\,h\right)$

$0$