  In this paper we study the behavior of a continuous time random walk (CTRW)
on a stationary and ergodic time varying dynamic graph. We establish conditions
under which the CTRW is a stationary and ergodic process. In general, the
stationary distribution of the walker depends on the walker rate and is
difficult to characterize. However, we characterize the stationary distribution
in the following cases: i) the walker rate is significantly larger or smaller
than the rate in which the graph changes (time-scale separation), ii) the
walker rate is proportional to the degree of the node that it resides on
(coupled dynamics), and iii) the degrees of node belonging to the same
connected component are identical (structural constraints). We provide examples
that illustrate our theoretical findings.
