The connectome of the brain has a great impact on the function of the brain as the structure of the connectome affects the speed and efficiency of information transfer. As a highly energy-consuming organ, an efficient network structure is essential. A previous study has shown consistent overall brain connectivity across a large variety of species. This connectivity conservation was explained by a balance between interhemispheric and intrahemispheric connections; that is, spices with highly connected hemispheres appear to have weaker interhemisphere connections. This study examines this connectivity trade-off in the human brain using diffusion-based tractography and network analysis in the Human Connectome Project (970 subjects, 527 female). We explore the biological origins of this phenomenon, heritability, and the effect on cognitive measures. The proportion of commissural fibers in the brain had a negative correlation to hemispheric efficiency, pointing to a tradeoff between inner hemispheric and interhemispheric connectivity. Network hubs including anterior and middle cingulate cortex, superior frontal areas, medial occipital areas, the parahippocampal gyrus, post- and precentral gyri, and the precuneus had the strongest contribution to this phenomenon. Other results show a high heritability as well as a strong connection to crystalized intelligence. This work presents cohort-based network analysis research, spanning a large variety of samples and exploring the overall architecture of the human connectome. Our results show a connectivity conservation phenomenon at the base of the overall brain network architecture. This network structure may explain much of the functional, behavioral, and cognitive variability among different brains.