We propose a unique, minimal assumption, approach based on variance analyses (compared with standard approaches) to investigate genetic influence on individual differences on the functional connectivity of the brain using 65 monozygotic and 65 dizygotic healthy young adult twin pairs' low‐frequency oscillation resting state fMRI data from the Human Connectome Project. Overall, we found high number of genetically‐influenced functional (GIF) connections involving posterior to posterior brain regions (occipital/temporal/parietal) implicated in low‐level processes such as vision, perception, motion, categorization, dorsal/ventral stream visuospatial, and long‐term memory processes; midline brain regions (cingulate) implicated in attentional processes, and emotional responses to pain. We found low number of GIF connections involving anterior to anterior/posterior brain regions (frontofrontal > frontoparietal, frontotemporal, frontooccipital) implicated in high‐level processes such as working memory, reasoning, emotional judgment, language, and action planning. We found very low number of GIF connections involving subcortical/noncortical networks such as basal ganglia, thalamus, brainstem, and cerebellum. In terms of sex‐specific individual differences, males were more genetically influenced while females were more environmentally influenced in terms of the interplay of interactions of Task positive networks (brain regions involved in various task‐oriented processes and attending to and interacting with environment), extended Default Mode Network (a central brain hub for various processes such as internal monitoring, rumination, and evaluation of self and others), primary sensorimotor systems (vision, audition, somatosensory, and motor systems), and subcortical/noncortical networks. There were >8.5‐19.1 times more GIF connections in males than females. These preliminary (young adult cohort‐specific) findings suggest that individual differences in the resting state brain may be more genetically influenced in males and more environmentally influenced in females; furthermore, based on standard approaches, environmental influences on individual differences may be substantially greater than that of genetics, for either sex, frontally and brain‐wide.