In this paper we address the use of graphical models for the analysis of the dynamic relations among the marginal processes of a time-homogeneous first order multivariate Markov chain. We employ a multi edge graph whose nodes represent the univariate marginal processes of the Markov chain and whose directed and bi-directed edges describe the dependence structure among them. The approach, adopted here, enables us to interpret the lack of directed edges as Granger-noncausal relationships (see Chamberlain, 1982) while missing bi-directed edges are used to visualize the contemporaneous independence relations between the marginal processes of the chain.