We propose two graphical models to represent a concise description of the causal statistical dependence structure between a group of coupled stochastic processes. The first, minimum generative model graphs, is motivated by generative models. The second, directed information graphs, is motivated by Granger causality. We show that under mild assumptions, the graphs are identical. In fact, these are analogous to Bayesian and Markov networks respectively, in terms of Markov blankets and I-map properties. Furthermore, the underlying variable dependence structure is the unique causal Bayesian network. Lastly, we present a method using minimal-dimension statistics to identify the structure when upper bounds on the in-degrees are known. Simulations show the effectiveness of the approach.