  The reciprocal class of a Markov path measure is the set of all mixtures of
its bridges. We give characterizations of the reciprocal class of a
continuous-time Markov random walk on a graph. Our main result is in terms of
some reciprocal characteristics whose expression only depends on the jump
intensity. We also characterize the reciprocal class by means of Taylor
expansions in small time of some conditional probabilities.
  Our measure-theoretical approach allows to extend significantly already known
results on the subject. The abstract results are illustrated by several
examples.
