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I have a simple tree graph with directed edges:

In: AdjacencyList[Graph[{a -> b, a -> c, b -> d, b -> e}], b]
Out: {a, d, e}

I wonder how I can select only the outgoing edge vertices elegantly.

{d, e}

In other words: I want the children of a vertex only.

The obvious solution for a tree is to always drop the first vertex. Sadly this approach fails for the root vertex, so there has to be some If-branching - which I want to avoid.

So far I tried VertexOutComponent and IncidenceList but non of them seems to give the option to filter by edge direction.

Do you see an elegant approach there, or will I have to keep using root checks?

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    $\begingroup$ With g = Graph[{a -> b, a -> c, b -> d, b -> e}]; you can do Last /@ EdgeList[g, b \[DirectedEdge] _]. $\endgroup$ Commented Jan 12, 2015 at 14:49
  • $\begingroup$ What did you try with VertexOutComponent? "but non of them seems to give the option to filter by edge direction" $\leftarrow$ actually it does, that's why it has "Out" in the name. $\endgroup$ Commented Jan 12, 2015 at 15:03
  • $\begingroup$ @Szabolcs I find this whole implementation really confusing. Why doesn't an AdjacencyList for a directed graph include only vertices that are adjacent to the vertex, not also those it is adjacent from. Wouldn't that be more standard? (E.g., xlinux.nist.gov/dads/HTML/adjacencyListRep.html) Somewhat similarly for the VertexOutComponent: why does the result for a vertex include that vertex when there is no self loop? Is there a standard reference that justifies this vocabulary? $\endgroup$ Commented Oct 2, 2015 at 16:07

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VertexOutComponent gives 

VertexOutComponent[g, b, 1]
(* {b, d, e} *)

This is precisely what you are looking for, plus the vertex b itself.

To retrieve the full adjacency list of a directed graph, you can also use IGAdjacencyList from IGraph/M.

g = Graph[{a -> b, a -> c, b -> d, b -> e}];

IGAdjacencyList[g, "Out"]
(* <|a -> {b, c}, b -> {d, e}, c -> {}, d -> {}, e -> {}|> *)

IGAdjacencyList[g, "In"]
(* <|a -> {}, b -> {a}, c -> {a}, d -> {b}, e -> {b}|> *)
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  • $\begingroup$ Ah, thank you very much. What confused me is that the vertex itself is included - as in my understanding its not exactly an out component. What I use now is Drop[VertexOutComponent[g, b, 1], 1]. This truly returns all vertices from out directed edges of b. $\endgroup$ Commented Jan 13, 2015 at 15:31
  • $\begingroup$ Aren't those duplicates? mathematica.stackexchange.com/questions/97044/… $\endgroup$ Commented Nov 17, 2015 at 12:04

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