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Degree returns the degree of v; that is, the number of edges of the graph G which are incident to v. The directions of the edges are ignored.

InDegree returns the in-degree of v; that is, the number of arcs directed into v.

OutDegree returns the out-degree of v; that is, the number of arcs directed out of v.

To find the vertices which are the tails of arcs directed into v, use GraphTheory[Arrivals] .

To find the vertices which are the heads of arcs directed out of v, use GraphTheory[Departures] .

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

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

$G≔\mathrm{Graph\; 1:\; a\; directed\; graph\; with\; 4\; vertices\; and\; 4\; arcs}$

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

$\mathrm{Degree}\left(G\,2\right)$

$3$

$\mathrm{InDegree}\left(G\,2\right)$

$2$

$\mathrm{OutDegree}\left(G\,2\right)$

$1$