The Subgraph command returns the subgraph formed by a specified set (or list) of edges.

To induce a subgraph using a set of vertices, use the InducedSubgraph command.

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

$\mathrm{K5}≔\mathrm{CompleteGraph}\left(5\right)$

$\mathrm{K5}≔\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 5\; vertices\; and\; 10\; edge(s)}$

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

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

$H≔\mathrm{Subgraph}\left(\mathrm{K5}\,E\right)$

$H≔\mathrm{Graph\; 2:\; an\; undirected\; unweighted\; graph\; with\; 4\; vertices\; and\; 4\; edge(s)}$

$\mathrm{evalb}\left(\mathrm{Edges}\left(H\right)=E\right)$

$\mathrm{true}$

$\mathrm{HighlightSubgraph}\left(\mathrm{K5}\,H\right)$

$\mathrm{DrawGraph}\left(\mathrm{K5}\right)$