  Graph models have long been used in lieu of real data which can be expensive
and hard to come by. A common class of models constructs a matrix of
probabilities, and samples an adjacency matrix by flipping a weighted coin for
each entry. Examples include the Erd\H{o}s-R\'{e}nyi model, Chung-Lu model, and
the Kronecker model. Here 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 order 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.
