Markov state models (MSMs) have proven themselves to be effective statistical and quantitative models for understanding protein folding dynamics. As stochastic networks, MSMs allow for descriptions of parallel folding pathways and facilitate quantitative comparison to experiments conducted at the ensemble level. While this complex network structure is advantageous in many respects, a simple topological description of these graphs is elusive. In this paper, we compare a series of protein folding MSMs to the topology of the Cayley tree, a graph structure on which dynamics are intuitive. We go on to introduce and test new sampling schemes that have potential to improve automated model construction, a critical step toward making Markov state modeling more accessible to general users.