Author Summary Using a graphical framework approach, our findings suggest that following awakening from slow wave sleep: (a) a prioritization scheme may underlie recovery rates for different behaviors; (b) long-range neural connections orchestrating local-global operations are uniquely disrupted; and (c) a peppermint odorant is able to minimize disruption to long-range connections. This research (a) advances the knowledge of neural processes during the transition from sleep to wakefulness and (b) applies a novel methodological approach to sleep-wake brain states. Further research is needed to apply this analytical method to alternative interventions and sleep-wake transition scenarios. Abstract Sleep inertia is the brief period of impaired alertness and performance experienced immediately after waking. Little is known about the neural mechanisms underlying this phenomenon. A better understanding of the neural processes during sleep inertia may offer insight into the awakening process. We observed brain activity every 15 min for 1 hr following abrupt awakening from slow wave sleep during the biological night. Using 32-channel electroencephalography, a network science approach, and a within-subject design, we evaluated power, clustering coefficient, and path length across frequency bands under both a control and intervention conditions. We found that under control conditions, the awakening brain is characterized by an immediate reduction in global theta, alpha, and beta power. Simultaneously, we observed a decrease in the clustering coefficient and an increase in path length within the delta band. Exposure to an odorant (i.e., peppermint) immediately after awakening ameliorated changes in clustering. Our results suggest that long-range network communication within the brain is crucial to the awakening process and that the brain may prioritize these long-range connections during this transitional state. Our study highlights a novel neurophysiological signature of the awakening brain and provides some initial evidence that may accelerate the process via interventions.