Recent connectomic tract tracing reveals that, contrary to what was previously thought, the cortical interareal network has high density. This leads to a necessary revision of the relevance of some of the graph theoretical notions, such as the Small-World property, hubs and Rich-Clubs that have been claimed to characterize the inter-areal cortical network. Weight and projection distance relationships of inter-areal connections inferred from consistent tract tracing data have recently led to the definition of a novel network model, the Exponential Distance Rule (EDR) model that predicts many observed local and global features of the cortex. The EDR model is a spatially embedded network whose properties are determined by the physical constraints on wiring and geometry, in sharp contrast with the purely topological graph models used heretofore in the description of the cortex. We speculate that when diving down to finer levels of the embedded cortical network, similar, physically constrained descriptions of connectivity may prove to be equally important for understanding cortical function.