Hello everyone!
I’ve a nested function I’m trying to examine, which may or may not branch at each point. It generates data looking like this:
\left\{1, \{2\}, \{\{3,4\}\}, \{\{\{5,6\},\{7\}\}\}\right\}
So above 2 has the image \{3,4\} and 3 in turn splits to \{5,6\}. Each element having higher depth than the last.
I want to graph these progressions, but I’m struggling to map vertex edges between my nodes automatically.
For The above example data the desired result is a list of directed edges pointing each node to its image, like so:
\left\{1\to 2,2\to 3,2\to 4,3\to
5,3\to 6,4\to 7\right\}
My attempts get tied up with successive tables very quickly. So I’m looking for any advice or examples to follow.
David
Is this what you are looking for?
In[1]:= tree = {1, {2}, {{3, 4}}, {{{5, 6}, {7}}}};
flat[v_] := If[ListQ[v], Flatten[v], {v}];
verts = Map[{flat[First[#]], flat[Last[#]]} &, Partition[tree, 2, 1]];
edgelist = Flatten[Map[Outer[DirectedEdge, Sequence @@ #] &, verts]]
Out[3]= {1 \[DirectedEdge] 2, 2 \[DirectedEdge] 3, 2 \[DirectedEdge] 4, 3 \[DirectedEdge] 5,
3 \[DirectedEdge] 6, 3 \[DirectedEdge] 7, 4 \[DirectedEdge] 5, 4 \[DirectedEdge] 6, 4 \[DirectedEdge] 7}
With a little bit of concentration and time it should be possible to simplify that even more.
That’s really great Bill! Thank you so much.
A few of these functions are a tad unfamiliar to me, so this will hopefully fuel me to get through these sorts of problems alone in future.
You should check that output very carefully to make certain it is doing what you want. I’m not convinced I really understand exactly what the function should do with all possible variations of your input.
What the function was trying to do was massage the input into a consistent form and then use Outer to generate all the edges from source to destination verticies.