Neighbors returns a list of lists if the input is just a graph. The ith list is the list of neighbors of the ith vertex of the graph. Neighbors(G, v) returns the list of neighbors of vertex v in the graph G.

Arrivals returns a list of the lists of vertices which are at the tail of arcs directed into vertex i. Undirected edges are treated as if they were bidirectional. If a vertex v is specified, the output is only the list of vertices which are at the tail of arcs directed into vertex v.

Departures is similar to Arrivals, but returns a list of the lists of vertices which are at the head of edges directed out of vertex i. If a vertex v is specified, the output is only the list of vertices which are at the head of edge directed out of vertex v.

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

$G≔\mathrm{Digraph}\left(\mathrm{Trail}\left(1\,2\,3\,4\,5\,6\,4\,7\,8\,2\right)\right)$

$G≔\mathrm{Graph\; 1:\; a\; directed\; graph\; with\; 8\; vertices\; and\; 9\; arc(s)}$

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

$\mathrm{Neighbors}\left(G\,4\right)$

$\left[3\,5\,6\,7\right]$

$\mathrm{Arrivals}\left(G\,4\right)$

$\left[3\,6\right]$

$\mathrm{Departures}\left(G\,4\right)$

$\left[5\,7\right]$

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

$\left[\left[2\right]\,\left[1\,3\,8\right]\,\left[2\,4\right]\,\left[3\,5\,6\,7\right]\,\left[4\,6\right]\,\left[4\,5\right]\,\left[4\,8\right]\,\left[2\,7\right]\right]$

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

$\left[\left[\right]\,\left[1\,8\right]\,\left[2\right]\,\left[3\,6\right]\,\left[4\right]\,\left[5\right]\,\left[4\right]\,\left[7\right]\right]$

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

$\left[\left[2\right]\,\left[3\right]\,\left[4\right]\,\left[5\,7\right]\,\left[6\right]\,\left[4\right]\,\left[8\right]\,\left[2\right]\right]$