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

翻译：不确定性原理是信号处理中的重要理论工具，它为信号的时频集中性提供了限制。在许多实际应用中，信号域具有复杂的非规则结构，可通过图结构进行描述。本文聚焦于图的全局不确定性原理，提出了图信号不确定性界与图特征向量非局域性之间的新联系。我们进一步推导了随机$d$-正则图的不确定性界，并给出了任意图的不确定性界的数值高效上下界逼近方法。