Sure. As I see MCMC it’s basically a mathematical trick that lets you sample from probability distributions even if you only know the relative probability of different samples. It’s based on the observation that some Markov processes have a stationary distribution that is identical to a distribution you may want to sample from. But you need to carefully construct the Markov process for that observation to hold, and the properties you need to ensure are most easily understood as properties of a random walk graph. So the interesting subset of Markov processes are most easily understood as such random walks on a graph.