This article explores the effects of a single bus perturbation in the electrical grid using a Graph Signal Processing (GSP) perspective. The perturbation is characterized by a sudden change in real-power load demand or generation. The study focuses on analyzing the spread of the perturbation throughout the grid and proposes a measure of spreadability based on GSP. Moreover, the global and local smoothness properties of the difference bus voltage angle graph signals are evaluated for understanding their embedded patterns of spreadability property. It is demonstrated that the global smoothness of the bus voltage angle graph signal follows a quadratic relationship with the perturbation strength, which helps in characterizing the critical perturbation strength after which the power flow diverges indicating a stressed system. The impact of a single bus perturbation on power system graph signals has been investigated through both analytical derivations using the DC power flow model and simulation using the AC power flow model. The results reveal that the proposed measure of spreadability as well as local and global smoothness properties of the graph signals are independent of the perturbation strength and instead mainly depend on the perturbation's location.