paths in a weighted directed trees

Question

Given an weighted directed tree, I have to write this:

Given a vertex v, I should list all the vertex c such that there exist a path whose origin is in c and whose end is in v

Given a vertex v, I should list all the vertex c such that there exist a path whose origin is in v and whose end is in c

What is the easiest way to do this in Mathematica?

Thanks very much.

Answer 1

ClearAll[vcIn, vcOut]
vcIn = Rest @ VertexInComponent @ ## &;
vcOut = Rest @ VertexOutComponent @ ## &;

Examples:

g = Graph[{1 -> 2, 2 -> 3, 3 -> 4}, VertexShapeFunction -> "Name"]

vcIn[g, 3]

{2, 1}

vcOut[g, 2]

{3, 4}

Answer 2

Like with all Graphs, you can use FindPath.

g = Graph[{1 -> 2, 2 -> 3, 3 -> 4}, VertexShapeFunction -> "Name"]
c = 1;
v = 3;
FindPath[g, c, v, ∞, 1]

{{1, 2, 3}}