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?
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3 Answers
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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.
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$\begingroup$ My graph is directed, and the function returns a set of neighbors of a certain vertex. $\endgroup$ Jun 20, 2019 at 19:28
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1$\begingroup$ @user2679290 Oops! I did not notice that detail. I adjusted my code to work in that case. Thanks for telling. $\endgroup$– SomosJun 20, 2019 at 19:55
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$\begingroup$ Yeh, Thread is essentially what I do in a seperate function $\endgroup$ Jun 20, 2019 at 21:36
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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]
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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
Needs["Combinatorica`"]before you can useFunctionalGraph. $\endgroup$Graph[(# <-> f[#]) & /@ v], wherefis your function andvare the vertices. $\endgroup$