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Uncertainty principles present an important theoretical tool in signalprocessing, as they provide limits on the time-frequency concentration of asignal. In many real-world applications the signal domain has a complicatedirregular structure that can be described by a graph. In this paper, we focuson the global uncertainty principle on graphs and propose new connectionsbetween the uncertainty bound for graph signals and graph eigenvectorsdelocalization. We also derive uncertainty bounds for random $d$-regular graphsand provide numerically efficient upper and lower approximations for theuncertainty bound on an arbitrary graph.

On Graph Uncertainty Principle and Eigenvector Delocalization