Arterial network topologies exhibit a hierarchical and self-similar organization, characterized by progressive changes in geometry and stiffness that define an arterial stiffness gradient (ASG). Aging and vascular diseases—such as hypertension and atherosclerosis—can disrupt the ASG, thereby altering hemodynamic behavior. This study investigates the impact of ASG alterations on arterial pressure waveform (APW) morphology using a generic one-dimensional hierarchical vascular model. The network incorporates variations in the constitutive arterial parameters to simulate both healthy and pathological conditions. Results demonstrate that changes in ASG significantly affect APW across arterial levels, highlighting the interplay between vascular structure and pressure dynamics. Given the clinical accessibility of APW at peripheral sites (e.g., carotid, radial), these findings support the utility of waveform-derived metrics for vascular assessment and monitoring.