In this paper, we introduce a new type of graphical model, interventional dependency graphs, to encode interactions among processes. These type of graphical models are defined using a measure that captures the influence relationships based on the principle of intervention. Principle of intervention discovers an influence relationship by making assignment to certain variables while fixing other variables to see how these changes influence statistics of variables of interest. Furthermore, we derive some properties of the dynamics that can be inferred from these graphs and establish the relationship between this new graphical model and the directed information graphs used for causal inference.