The HighlightedEdges command returns a set (which may be empty) of the edges of a graph G that have been highlighted.

An edge is considered to have been highlighted if it is to be drawn with a color other than the default.

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

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

$\mathrm{HighlightedEdges}\left(G\right)$

$\varnothing$

$T≔\mathrm{SpanningTree}\left(G\right)\:$

$\mathrm{HighlightEdges}\left(G\,\mathrm{Edges}\left(T\right)\,''Red''\right)$

$\mathrm{HighlightedEdges}\left(G\right)$

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