Functional connectivity has attracted significant interest in the identification of specific circuits underlying brain (dys-)function. Classical analyses to estimate functional connectivity (i.e., filtering electrophysiological signals in canonical frequency bands and using connectivity metrics) assume that these reflect oscillatory networks. However, this approach conflates non-oscillatory, aperiodic neural activity with oscillations; raising the possibility that these functional networks may reflect aperiodic rather than oscillatory activity. Here, we provide the first study quantifying, in two different human electroencephalography (EEG) databases, the contribution of aperiodic activity on reconstructed oscillatory functional networks in resting state. We found that more than 99% of delta, theta, and gamma functional networks, more than 90% of beta functional networks and between 23 and 55% of alpha functional networks were actually driven by aperiodic activity. While there is no universal consensus on how to identify and quantify neural oscillations, our results demonstrate that oscillatory functional networks are drastically sparser than commonly assumed. These findings suggest that most functional connectivity studies focusing on resting state actually reflect aperiodic networks instead of oscillations-based networks. We highly recommend that oscillatory network analyses first check the presence of aperiodicity-unbiased neural oscillations before estimating their statistical coupling to strengthen the robustness, interpretability, and reproducibility of functional connectivity studies.