Small-world networks provide an appealing description of cortical architecture owing to their capacity for integration and segregation combined with an economy of connectivity. Previous reports of low-density interareal graphs and apparent small-world properties are challenged by data that reveal high-density cortical graphs in which economy of connections is achieved by weight heterogeneity and distance-weight correlations. These properties define a model that predicts many binary and weighted features of the cortical network including a core-periphery, a typical feature of self-organizing information processing systems. Feedback and feedforward pathways between areas exhibit a dual counterstream organization, and their integration into local circuits constrains cortical computation. Here, we propose a bow-tie representation of interareal architecture derived from the hierarchical laminar weights of pathways between the high-efficiency dense core and periphery.