The idea that intelligence is embedded not only in a single brain network, but instead in a complex, well-optimized system of complementary networks, has led to the development of whole brain network analysis. Using graph theory to analyze resting-state functional MRI data, we investigated the brain graph networks (or brain networks) of high intelligence quotient (HIQ) children. To this end, we computed the "hub disruption index κ," an index sensitive to graph network modifications. We found significant topological differences in the integration and segregation properties of brain networks in HIQ compared to standard IQ children, not only for the whole brain graph, but also for each hemispheric graph, and for the homotopic connectivity. Moreover, two profiles of HIQ children, homogenous and heterogeneous, based on the differences between the two main IQ subscales [verbal comprehension index (VCI) and perceptual reasoning index (PRI)], were compared. Brain network changes were more pronounced in the heterogeneous than in the homogeneous HIQ subgroups. Finally, we found significant correlations between the graph networks' changes and the full-scale IQ (FSIQ), as well as the subscales VCI and PRI. Specifically, the higher the FSIQ the greater was the brain organization modification in the whole brain, the left hemisphere, and the homotopic connectivity. These results shed new light on the relation between functional connectivity topology and high intelligence, as well as on different intelligence profiles.