Recurrent neural networks can be modeled as dynamical systems on directed graphs. What graph features are important for shaping the emergent dynamics? In this talk we will introduce the concept graphical domination and present key theorems about domination that help us understand the associated nonlinear dynamics. In particular, domination can be used to reduce graphs to smaller equivalent networks. We also show how reducible graph modules can be chained together to produce larger networks with predictable dynamics. These networks are amenable to control via inhibitory pulses. While these results were originally developed for a special class of effectively inhibitory threshold-linear networks, we will show how they apply equally well to E-I networks with global inhibition.