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I have a directed graph $G_1$. I extract its transition matrix $T_1$.

Now I also have directed graph $G_2$, which is equal to $G_1$ with inverted edges. If I get its transition matrix $T_2$, what is the relationship between $T_1$ and $T_2$?

What is the relationship between the adjancency matrices of $G_1$ and $G_2$?

Thanks for any hint, Mulone

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    Are you *asking* us if $T_2$ is the inverse of $T_1$, or are you stating it?2011-09-01
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    It won't be the inverse. Consider: if the digraph is a directed path $a \to b \to c$, its adjacency matrix isn't invertible; but the reversed digraph certainly does have an adjacency matrix. —— Why don't you take a look at some simple examples, like short directed paths, and see if anything jumps out at you?2011-09-01
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    I've updated the question2011-09-02

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Hint: $T_1$ has a $1$ in the $i,j$ location if there is a path from $V_i$ to $V_j$