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<p>Since humans spend large amounts of time sleeping, it is natural and important for us to study and understand the mechanisms involved. Specifically, the mechanisms underlying sleep-wake transitions are not well understood. It has been reported that the wake bouts for humans follow a power law distribution, while sleep bouts follow an exponential distribution. In this project, we aim to gain a better understanding of the power laws produced by a stochastic competitive graph model, which could be relevant for the study of the human wake bouts. We are studying how the power law scaling exponent varies with the structure of the random graph and with the excitatory and inhibitory degrees of the nodes. Additionally, we consider different methods for calculating bouts, based on how the transition interval into (or out of) wake is treated.</p>