  The concept of intransitiveness for games, which is the condition for which
there is no first-player winning strategy can arise surprisingly, as happens in
the Penney game, an extension of the heads or tails. Since a game can be
converted into a random walk on a graph, i.e., a Markov process, we extend the
intransitiveness concept to such systems. The end of the game generally
consists in the appearance of a pre-defined pattern. In the language of random
walk this corresponds to an absorbing trap, since once that the game has
reached this condition the game comes to an end. Therefore, the
intransitiveness of the game can be mapped into a problem of competition among
traps. We analyse in details random walkers on several kind of networks (rings,
scale-free, hierarchical and city-inspired) with several variations: traps can
be partially absorbing, the walker can be biased and the initial distribution
can be arbitrary. We found that the transitivity concept can be quite useful
for characterizing the combined properties of a graph and that of the walkers.
