Bumpless pipe dreams (BPDs) are combinatorial objects introduced in 2018 to study Schubert polynomials. Using results from the literature, we introduce a graph structure on the set of BPDs for a fixed permutation, where the edges are determined by certain local moves. We implemented these objects in SageMath and used our program to generate all 409,113 graphs for small permutations. We analyzed this data to form a conjecture on which permutations have acyclic graphs, which we proved using induction. In this talk, we give a pattern-avoidance condition that is necessary for a permutation’s BPD graph to be a tree.