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Heritability and genetic covariance/correlation quantify the marginal and shared genetic effects across traits. They offer insights on the genetic architecture of complex traits and diseases. To explore how genetic variations contribute to brain function variations, we estimated heritability and genetic correlation across cortical thickness, surface area, and volume of 33 anatomically predefined regions in left and right hemispheres, using summary statistics of genome-wide association analyses of 31,968 participants in the UK Biobank. To characterize the relationships between these regions of interest, we constructed a genetic network for these regions using recursive two-way cut-offs in similarity matrices defined by genetic correlations. The inferred genetic network matches the brain lobe mapping more closely than the network inferred from phenotypic similarities. We further studied the associations between the genetic network for brain regions and 30 complex traits through a novel composite-linkage disequilibrium score regression method. We identified seven significant pairs, which offer insights on the genetic basis for regions of interest mediated by cortical measures., Competing Interests: Declaration of competing interest The authors declare that they have no conflict of interest., (Copyright © 2024 The Authors. Published by Elsevier Inc. All rights reserved.)