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In the present paper we show that for any given digraph $\mathbb{G} =([n],\vec{E})$, i.e. an oriented graph without self-loops and 2-cycles, one canconstruct a 1-dependent Markov chain and $n$ identically distributed hittingtimes $T_1, \ldots , T_n $ on this chain such that the probability of the event$T_i > T_j $, for any $i, j = 1, \ldots n$, is larger than $\frac{1}{2}$ if andonly if $(i,j)\in \vec{E}$. This result is related to various paradoxes inprobability theory, concerning in particular non-transitive dice.

Ranking graphs through Markov chains and hitting times