Graphical programming or modeling environments, such as a block diagram environment, are disclosed in which dependencies that influence how a model executes are defined without altering the visual representation of the model. In the graphical modeling or programming environment, users create a model that describes how the system is to execute. The users can then augment the model with non-graphical dependencies that provide general execution goals or specific dependencies between blocks. The user can augment the graphical model with dependency constraints specifying how the model should execute. The constraints are coupled to the model and can be optionally displayed on the model in a debugging/analysis mode to provide further insight into how the model executes.