A major challenge in neuroscience is finding which genes affect brain integrity, connectivity, and intellectual function. Discovering influential genes holds vast promise for neuroscience, but typical genome-wide searches assess around one million genetic variants one-by-one, leading to intractable false positive rates, even with vast samples of subjects. Even more intractable is the question of which genes interact and how they work together to affect brain connectivity. Here we report a novel approach that discovers which genes contribute to brain wiring and fiber integrity at all pairs of points in a brain scan. We studied genetic correlations between thousands of points in human brain images from 472 twins and their non-twin siblings (mean age: 23.7±2.1 SD years; 193 M/279 F). We combined clustering with genome-wide scanning to find brain systems with common genetic determination. We then filtered the image in a new way to boost power to find causal genes. Using network analysis, we found a network of genes that affect brain wiring in healthy young adults. Our new strategy makes it more computationally tractable to discover genes that affect brain integrity. The gene network showed small-world and scale-free topologies, suggesting efficiency in genetic interactions, and resilience to network disruption. Genetic variants at hubs of the network influence intellectual performance by modulating associations between performance intelligence quotient (IQ) and the integrity of major white matter tracts, such as the callosal genu and splenium, cingulum, optic radiations, and the superior longitudinal fasciculus.