This is the first study investigating the genetics of weighted functional brain network graph theory measures from 18,445 participants of the UK Biobank (44-80 years). The eighteen measures studied showed low heritability (mean h2SNP =0.12) and were highly genetically correlated. Genome-wide association studies for these measures observed 14 significant variants associated with strength of somatomotor and limbic networks. These intergenic variants were located near the PAX8 gene on chromosome 2. Gene-based analyses identified five significantly associated genes for five of the network measures, which have been implicated in sleep duration, neuronal differentiation/development, cancer, and susceptibility to neurodegenerative diseases. Genetic correlations with other traits were examined and significant correlations were observed with sleep measures and psychiatric symptoms. Further analysis found that somatomotor network strength was phenotypically associated with sleep duration and insomnia. Single nucleotide polymorphism (SNP) and gene level associations with functional network measures were identified, which may help uncover novel biological pathways relevant to human brain functional network integrity and diseases that affect it. ### Competing Interest Statement The authors have declared no competing interest.

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