  We show that, for every positive real number h and every positive integer p,
there exist oriented graphs G, G' (with countably many vertices) that are
strongly connected, of period p, of Gurevich entropy h, such that G is positive
recurrent (thus the topological Markov chain on G admits a measure of maximal
entropy) and G' is transient (thus the topological Markov chain on G' admits no
measure of maximal entropy).
