Cognition is based on the integrated functioning of hierarchically organized cortical processing streams in a manner yet to be clarified. Because integration fundamentally depends on convergence and the complementary notion of divergence of the neuronal connections, we analysed integration by measuring the degree of convergence/divergence through the connections in the network of cortical areas. By introducing a new index, we explored the complementary convergent and divergent nature of connectional reciprocity and delineated the backward and forward cortical sub-networks for the first time. Integrative properties of the areas defined by the degree of convergence/divergence through their afferents and efferents exhibited distinctive characteristics at different levels of the cortical hierarchy. Areas previously identified as hubs exhibit information bottleneck properties. Cortical networks largely deviate from random graphs where convergence and divergence are balanced at low reciprocity level. In the cortex, which is dominated by reciprocal connections, balance appears only by further increasing the number of reciprocal connections. The results point to the decisive role of the optimal number and placement of reciprocal connections in large-scale cortical integration. Our findings also facilitate understanding of the functional interactions between the cortical areas and the information flow or its equivalents in highly recurrent natural and artificial networks.