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networks

 spanpoly
 span polynomial of an undirected graph

 Calling Sequence spanpoly(G, p)

Parameters

 G - undirected graph or network p - variable in span poly (usually edge probability)

Description

 • 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](...).

Examples

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

 > $\mathrm{with}\left(\mathrm{networks}\right):$
 > $G≔\mathrm{complete}\left(4\right):$
 > $\mathrm{addedge}\left(\left\{\left\{1\right\},\left\{1,2\right\}\right\},G\right):$
 > $\mathrm{spanpoly}\left(G,p\right)$
 ${{p}}^{{3}}{}\left({6}{}{{p}}^{{4}}{-}{32}{}{{p}}^{{3}}{+}{66}{}{{p}}^{{2}}{-}{63}{}{p}{+}{24}\right)$ (1)
 > $\mathrm{spanpoly}\left(G,\frac{1}{2}\right){2}^{\mathrm{nops}\left(\mathrm{edges}\left(G\right)\right)}$
 ${172}$ (2)