Deoxyribonucleic Acid (DNA) is proven to be a valuable building block for constructing nanostructures capable of targeted drug delivery. DNA is also characterized as self-assembling; when a sticky end is introduced to complementary unbonded base pairs, DNA will hydrogen bond without any mechanical assistance. Graph theory can be implemented to model this phenomenon, and one such framework is referred to as the flexible tile model of DNA self-assembly. This model allows for symmetry and predicted bonding where it may not exist in the lab setting. We add to the flexible tile model in order to calculate the probability of self-assembly of certain graphs. If a specific graph type or family is desired, or even a single specific graph, the probability of this event occurring can be calculated. This theoretical experiment explores the possibility and probability that cohesive end types, in the flexible tile model, can bond to other end types when exposed to one another in a lab setting. This exploration specifically focused on small cycle graphs of order three and four.