  We present a geometrically enhanced Markov chain Monte Carlo sampler for
networks based on a discrete curvature measure defined on graphs. Specifically,
we incorporate the concept of graph Forman curvature into sampling procedures
on both the nodes and edges of a network explicitly, via the transition
probability of the Markov chain, as well as implicitly, via the target
stationary distribution, which gives a novel, curved Markov chain Monte Carlo
approach to learning networks. We show that integrating curvature into the
sampler results in faster convergence to a wide range of network statistics
demonstrated on deterministic networks drawn from real-world data.
