The organizational principles that distinguish the human brain from other species have been a long-standing enigma in neuroscience. Focusing on the uniquely evolved human cortical layers 2 and 3, we computationally reconstruct the cortical architecture for mice and humans. Human neurons form highly complex networks demonstrated by their increased number and simplex dimension compared to mice. This is surprising because human pyramidal cells are much sparser. The number and size of neurons cannot account for this increased network complexity, suggesting that another morphological property is a key determinant of network connectivity. The topological comparison of the dendritic structure reveals higher perisomatic density in human pyramidal cells. We quantitatively show that this neuronal structural property directly impacts network complexity, including the formation of a rich subnetwork structure. Therefore, greater dendritic complexity, a defining attribute of human pyramidal cells, may provide the human cortex with enhanced computational capacity and cognitive flexibility.