Propagation graphs (PGs) serve as a frequency-selective, spatially consistent channel model suitable for fast channel simulations in a scattering environment. So far, however, the parametrization of the model, and its consequences, have received little attention. In this contribution, we propose a new parametrization for PGs that adheres to the doubly exponentially decaying cluster structure of the Saleh-Valenzuela (SV) model. We show how to compute the newly proposed internal model parameters based on an approximation of the $K$-factor and the two decay rates from the SV model. Furthermore, via the singular values of multiple-input multiple-output (MIMO) channels, we compare the degrees of freedom (DoF) between our new and another frequently used parametrization. Specifically, we compare the DoF loss when the distance between antennas within the transmitter and receiver arrays or the average distance between scatterers decreases. Based on this comparison, it is shown that, in contrast to the typical parametrization, our newly proposed parametrization loses DoF in both scenarios, as one would expect from a spatially consistent channel model.