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Given a directed graph representing a relation $S$ on a finite set $F$. How do I draw the directed graphs representing the relation $S^2$, $S^3$, $\ldots$? Thanks!

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If $S$ has an arrow from $a$ to $b$ and another arrow from $b$ to $c$, then $S^2$ has an arrow from $a$ to $c$. If $S$ has an arrow from $a$ to $b$ and another arrow from $b$ to $c$ and yet another from $c$ to $d$, then $S^3$ has an arrow from $a$ to $d$.

(Somehow it seems as if, if that's not clear, you might be better off asking what the expressions $S^2$ and $S^3$ mean.)

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Thank you so much. :) – drawar Nov 19 '12 at 15:44

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