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

This routine creates a subgraph of G from either a set of vertices and their incident edges or a set of edges and their ends.

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

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

$G≔\mathrm{complete}\left(5\right)\:$

$\mathrm{induce}\left(\left\{1\,2\,3\,4\right\}\,G\right)$

$\mathbf{proc}\left(x\right)\mathbf{option}\mathrm{GRAPH}\,2\;\mathbf{if}x\=\mathrm{\_Edges}\mathbf{then}\mathrm{thisproc}\left(\mathrm{\_Edges}\right)≔\left\{\right\}\mathbf{elif}x\=\mathrm{\_EdgeIndex}\mathbf{then}\mathrm{thisproc}\left(\mathrm{\_EdgeIndex}\right)≔\mathrm{table}\left(\mathrm{symmetric}\right)\mathbf{elif}x\=\mathrm{\_Head}\mathbf{then}\mathrm{thisproc}\left(\mathrm{\_Head}\right)≔\mathrm{table}\left(\right)\mathbf{elif}x\=\mathrm{\_Tail}\mathbf{then}\mathrm{thisproc}\left(\mathrm{\_Tail}\right)≔\mathrm{table}\left(\right)\mathbf{elif}x\=\mathrm{\_Eweight}\mathbf{then}\mathrm{thisproc}\left(\mathrm{\_Eweight}\right)≔\mathrm{table}\left(\right)\mathbf{elif}x\=\mathrm{\_Ends}\mathbf{then}\mathrm{thisproc}\left(\mathrm{\_Ends}\right)≔\mathrm{table}\left(\right)\mathbf{elif}x\=\mathrm{\_Vertices}\mathbf{then}\mathrm{thisproc}\left(\mathrm{\_Vertices}\right)≔\left\{\right\}\mathbf{elif}x\=\mathrm{\_Vweight}\mathbf{then}\mathrm{thisproc}\left(\mathrm{\_Vweight}\right)≔\mathrm{table}\left(\mathrm{sparse}\right)\mathbf{elif}x\=\mathrm{\_Ancestor}\mathbf{then}\mathrm{thisproc}\left(\mathrm{\_Ancestor}\right)≔\mathrm{table}\left(\right)\mathbf{elif}x\=\mathrm{\_Daughter}\mathbf{then}\mathrm{thisproc}\left(\mathrm{\_Daughter}\right)≔\mathrm{table}\left(\right)\mathbf{elif}x\=\mathrm{\_Neighbors}\mathbf{then}\mathrm{thisproc}\left(\mathrm{\_Neighbors}\right)≔\mathrm{table}\left(\right)\mathbf{elif}x\=\mathrm{\_Status}\mathbf{then}\mathrm{thisproc}\left(\mathrm{\_Status}\right)≔\left\{\'\mathrm{SIMPLE}\'\right\}\mathbf{elif}x\=\mathrm{\_Emaxname}\mathbf{then}\mathrm{thisproc}\left(\mathrm{\_Emaxname}\right)≔0\mathbf{else}\mathbf{return}\'\mathrm{procname}\left(\mathrm{args}\right)\'\mathbf{end\; if}\mathbf{end\; proc}$

$\mathrm{ends}\left(\right)$

$\left\{\left\{1\,2\right\}\,\left\{1\,3\right\}\,\left\{1\,4\right\}\,\left\{2\,3\right\}\,\left\{2\,4\right\}\,\left\{3\,4\right\}\right\}$

$H≔\mathrm{induce}\left(\mathrm{incident}\left(1\,G\right)\,G\right)\:$

$\mathrm{ends}\left(H\right)$

$\left\{\left\{1\,2\right\}\,\left\{1\,3\right\}\,\left\{1\,4\right\}\,\left\{1\,5\right\}\right\}$