I've been working on taking sentences, converting morphemes into nodes and then having edges connecting the nodes in the different possible syntactically correct orders of a sentence. However, in doing this, the graphs that I create sometimes look like they allow for infinite cycles whereas in fact they do not. For example, I have this graph
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which would seem to imply that there is a cycle $\sigma(V,I,D)$, which does not exist. Is there a way to indicate that only certain paths are possible and that no cycles exist? What I'm trying to show is that $S$ must be the origination and from $S$ you can go to $V$, $I$, or $D$. Then from each of those you can go to the other two in certain orders. The paths I'm trying to graph are as such \begin{align} S \to I \to D \to V \\ S \to I \to V \to D \\ S \to D \to V \to I \\ S \to V \to D \to I \end{align} From the included graph all of those paths can be followed, but other non-existent paths can also be followed. Is there a better way to notate these specific paths within the above graph or is there a different methodology that should be used?

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    $\begingroup$ Presumably the paths are always of length 4. And just to clarify, SVID and SDIV are not allowed? $\endgroup$ – bvy Dec 4 '16 at 18:36
  • $\begingroup$ @bvy The paths are always of length 4. Yes $S\to V\to I\to D$ and $S\to D\to I\to V$ are not allowed. $\endgroup$ – Eli Sadoff Dec 4 '16 at 18:43
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    $\begingroup$ The rules suggest a tree, but you probably don't want multiple vertices representing a single morpheme. I don't see a way to model this with a simple digraph. Perhaps some sort of flow network, but it's not my area of expertise. $\endgroup$ – bvy Dec 4 '16 at 19:24
  • $\begingroup$ Ok but why is $S \to V \to I \to D$ (for example) not allowed? What is the rule? Because as I see it, you are allowed to move from $V \to I$, but only under special circumstances. (agree with bvy that it seems simple digraphs are not the best way to represent) $\endgroup$ – Morgan Rodgers Dec 4 '16 at 19:24
  • $\begingroup$ @MorganRodgers I'm mapping a french grammatical structure. So you can't for example say "J'ai donné à toi ça" because that doesn't follow grammatical rules whereas "J'ai donné ça à toi" does. $\endgroup$ – Eli Sadoff Dec 4 '16 at 19:30

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