With broad lines and dark shading, the cartographic depictions of ancient states and empires convey the impression of comprehensive political entities having firm boundaries and uniform territorial control. These depictions oversimplify the complexities of early state growth, as well as overstating the capacity of central governments to control large territories. Archaeological and textual evidence suggests that ancient states are better understood through network models rather than bounded-territory models. Network approaches enable us to depict competition within and among polities as they grow, the efficient use of nodal points as a focus for political leaders, and the realities of nonoverlapping ritual, social, and economic activities that have an impact on political cohesion. Network maps and bounded-territory representations are compared for the Inka, Mauryan, and Sassanian polities.