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

The acyclicity polynomial in variable p gives the probability that G is acyclic when each edge operates with probability p.

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

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

$G≔\mathrm{complete}\left(4\right)\:$

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

$\mathrm{acycpoly}\left(G\,p\right)$

$-{\left(-1+p\right)}^5\left(10p^3+9p^2+4p+1\right)$

$\mathrm{acycpoly}\left(G\,\frac{1}{2}\right)2^{\mathrm{nops}\left(\mathrm{edges}\left(G\right)\right)}$

$52$