Recent advances in connectomic and neurophysiological tools make it possible to probe whole-brain mechanisms in the mouse that underlie cognition and behavior. Based on experimental data, we developed a large-scale model of the mouse brain for a cardinal cognitive function called working memory, the brain’s ability to internally hold and process information without sensory input. In the model, interregional connectivity is constrained by mesoscopic connectome data. The density of parvalbumin-expressing interneurons in the model varies systematically across the cortex. We found that the long-range cell type-specific targeting and density of cell classes define working memory representations. A core cortical subnetwork and the thalamus produce distributed persistent activity, and the network exhibits numerous attractor states. Novel cell type-specific graph theory measures predicted the activity patterns and core subnetwork. This work highlights the need for cell type-specific connectomics, and provides a theory and tools to interpret large-scale recordings of brain activity during cognition.