IncidentEdges returns the set of edges (arcs) which are incident to a given vertices.  If G is a directed graph, then the set of arcs which have a tail in the given list of vertices are returned.

IncidentEdges(G, V, direction=incoming) returns the set of arcs which have a head in the given set of vertices.

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

$G≔\mathrm{CycleGraph}\left(7\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 7\; vertices\; and\; 7\; edge(s)}$

$\mathrm{IncidentEdges}\left(G\,1\right)$

$\left\{\left\{1\,2\right\}\,\left\{1\,7\right\}\right\}$

$\mathrm{IncidentEdges}\left(G\,\left[1\,5\,7\right]\right)$

$\left\{\left\{1\,2\right\}\,\left\{1\,7\right\}\,\left\{4\,5\right\}\,\left\{5\,6\right\}\,\left\{6\,7\right\}\right\}$

$\mathrm{DG}≔\mathrm{Digraph}\left(\mathrm{Trail}\left(1\,2\,3\,4\,5\,3\right)\,\mathrm{Trail}\left(1\,5\,2\,4\,1\right)\right)$

$\mathrm{DG}≔\mathrm{Graph\; 2:\; a\; directed\; graph\; with\; 5\; vertices\; and\; 9\; arc(s)}$

$\mathrm{IncidentEdges}\left(\mathrm{DG}\,\left[2\,3\right]\right)$

$\left\{\left[2\,3\right]\,\left[2\,4\right]\,\left[3\,4\right]\right\}$

$\mathrm{IncidentEdges}\left(\mathrm{DG}\,\left[2\,3\right]\,\mathrm{direction}=\mathrm{incoming}\right)$

$\left\{\left[1\,2\right]\,\left[2\,3\right]\,\left[5\,2\right]\,\left[5\,3\right]\right\}$