The human brain varies across individuals in its morphology, function, and cognitive capacities. Variability is particularly high in phylogenetically modern regions associated with higher order cognitive abilities, but its relationship to the layout and strength of functional networks is poorly understood. In this study we disentangled the variability of two key aspects of functional connectivity: strength and topography. We then compared the genetic and environmental influences on these two features. Genetic contribution is heterogeneously distributed across the cortex and differs for strength and topography. In heteromodal areas genes predominantly affect the topography of networks, while their connectivity strength is shaped primarily by random environmental influence such as learning. We identified peak areas of genetic control of topography overlapping with parts of the processing stream from primary areas to network hubs in the default mode network, suggesting the coordination of spatial configurations across those processing pathways. These findings provide a detailed map of the diverse contribution of heritability and individual experience to the strength and topography of functional brain architecture.