Here, we explore the impact of different graph traversal algorithms on molecular graph generation. We do this by training a graph-based deep molecular generative model to build structures using a node order determined via either a breadth- or depth-first search algorithm. What we observe is that using a breadth-first traversal leads to better coverage of training data features compared to a depth-first traversal. We have quantified these differences using a variety of metrics on a data set of natural products. These metrics include percent validity, molecular coverage, and molecular shape. We also observe that by using either a breadth- or depth-first traversal it is possible to overtrain the generative models, at which point the results with either graph traversal algorithm are identical.