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

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

When G is connected, this is the all-terminal reliability polynomial of G, and gives the probability that G is connected when each edge operates independently with probability p.

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

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

$G≔\mathrm{complete}\left(4\right)\:$

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

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

$p^3\left(6p^4-32p^3+66p^2-63p+24\right)$

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

$172$