The limited ability to simultaneously perform multiple tasks is one of the most salient features of human performance and a defining characteristic of controlled processing. Based on the assumption that multitasking constraints arise from shared representations between individual tasks, we describe a graph-theoretic approach to analyze these constraints. Our results are consistent with previous numerical work (Feng et al., 2014), showing that even modest amounts of shared representation induce dramatic constraints on the parallel processing capability of a network architecture. We further illustrate how this analysis method can be applied to specific neural networks to efficiently characterize the full profile of their parallel processing capabilities. We present simulation results that validate theoretical predictions, and discuss how these methods can be applied to empirical studies of controlled vs. and automatic processing and multitasking performance in humans.