The functional activation pattern within the human brain is known to change at varying time-scales. This existence of and dynamics between inherently different brain functional states are found to be related to human learning, behavior, and development, and, are therefore of high importance. Yet, tools to automatically identify such cognitive states are limited. In this study, we consider high-dimensional functional connectome data constructed from BOLD fMRI over short time-intervals as a graph, each time-point as a node, and the similarity between two time-points as the edge between those two nodes. We apply graph embedding techniques to automatically extract clusters of time-points, which represent canonical brain states. Application of graph embedding technique to BOLD fMRI time-series of a population comprised of autistic and neurotypical subjects demonstrates that two-layer embedding by preserving the higherorder similarity between different time-points is crucial toward successful identification of low-dimensional brain functional states. Finally, the present study reveals inherent existence of two brain meta-states within human brain.