The primate cortical visual system is composed of many structurally and functionally distinct areas or processing compartments, each of which receives on average about ten afferent inputs from other cortical areas and sends about the same number of output projections. The visual cortex is thus served by a very large number of cortico-cortical connections, so that the areas and their interconnections form a network of remarkable complexity. The gross organization of this cortical processing system hence represents a formidable topological problem: while the spatial position of the areas in the brain are becoming fairly well established, the gross `processing architecture,' defined by the connections, is much less well understood. I have applied optimization analysis to connectional data on the cortical visual system to address this topological problem. This approach gives qualitative and quantitative insight into the connectional topology of the primate cortical visual system and provides new evidence supporting suggestions that the system is divided into a dorsal `stream' and a ventral `stream' with limited cross-talk, that these two streams reconverge in the region of the principal sulcus (area 46) and in the superior temporal polysensory areas, that the system is hierarchically organized, and that the majority of the connections are from nearest-neighbor and next-door- but-one areas. The robustness of the results is shown by reanalyzing the connection data after various manipulations that simulate gross changes to the neuroanatomical database.