Abstract Time-varying changes in whole-brain connectivity patterns, or connectome state dynamics, are a prominent feature of brain activity with broad functional implications. While infra-slow (<0.1 Hz) connectome dynamics have been extensively studied with fMRI, rapid dynamics highly relevant for cognition are poorly understood. Here, we asked whether rapid electrophysiological connectome dynamics constitute subject-specific brain traits and to what extent they are under genetic influence. Using source-localized EEG connectomes during resting-state (N = 928, 473 females), we quantified heritability of multivariate (multi-state) features describing temporal or spatial characteristics of connectome dynamics. States switched rapidly every ∼60–500 ms. Temporal features were heritable, particularly, Fractional Occupancy (in theta, alpha, beta, and gamma bands) and Transition Probability (in theta, alpha, and gamma bands), representing the duration spent in each state and the frequency of state switches, respectively. Genetic effects explained a substantial proportion of phenotypic variance of these features: Fractional Occupancy in beta (44.3%) and gamma (39.8%) bands and Transition Probability in theta (38.4%), alpha (63.3%), beta (22.6%), and gamma (40%) bands. However, we found no evidence for heritability of dynamic spatial features, specifically states’ Modularity and connectivity pattern. We conclude that genetic effects shape individuals’ connectome dynamics at rapid timescales, specifically states’ overall occurrence and sequencing.