The heterogeneity of molecular mechanisms, target neural circuits, and neurophysiologic effects of general anesthetics makes it difficult to develop a reliable and drug-invariant index of general anesthesia. No single brain region or mechanism has been identified as the neural correlate of consciousness, suggesting that consciousness might emerge through complex interactions of spatially and temporally distributed brain functions. The goal of this review article is to introduce the basic concepts of networks and explain why the application of network science to general anesthesia could be a pathway to discover a fundamental mechanism of anesthetic-induced unconsciousness. This article reviews data suggesting that reduced network efficiency, constrained network repertoires, and changes in cortical dynamics create inhospitable conditions for information processing and transfer, which lead to unconsciousness. This review proposes that network science is not just a useful tool but a necessary theoretical framework and method to uncover common principles of anesthetic-induced unconsciousness.