Generate a graph from function on the vertices

Question

I have a concrete function $f:V\rightarrow P(V)$ that describes the neighborhood of a vertex $g$. I tried to use FunctionalGraph[f, V] , but apparently, this function was removed from Mathematica.

So, how to generate a graph from a function?

Answer 1

All you need is something like the code

ClearAll[f, V, a, b, c, d]; V = {a, b, c, d};
f[a] = {b}; f[b] = {c}; f[c] = {a, d}; f[d] = {c};
Graph[Flatten[Function[x, x -> # & /@ f[x]] /@ V]]

which returns a directed graph. A variant is to replace the last line with

Graph[Flatten[(Thread[# -> f[#]]) & /@ V]]

and there are probably a few other ways to do it.

Answer 2

You can also use RelationGraph with MemberQ[f@#, #2]& as the first argument:

Using Somos's example:

vl = {a, b, c, d};
f[a] = {b}; f[b] = {c}; f[c] = {a, d}; f[d] = {c};
RelationGraph[MemberQ[f @ #, #2]&, vl]

Answer 3

Well, the code is

JJ[a_]:=Map[(a->#)&,f[a]]
j=Graph[Flatten[JJ  /@V]]

As the code suggested by @user6014 ignores the nested sets