In this manuscript we present the HyperKron Graph model: an extension of the Kronecker Model, but with a distribution over hyperedges. We prove that we can efficiently generate graphs from this model in time proportional to the number of edges times a small log-factor, and find that in practice the runtime is linear with respect to the number of edges. We illustrate a number of useful features of the HyperKron model including non-trivial clustering and highly skewed degree distributions. Finally, we fit the HyperKron model to real-world networks, and demonstrate the model's flexibility with a complex application of the HyperKron model to networks with coherent feed-forward loops.