A pure hypothesis test for inhomogeneous random graph models based on a kernelised Stein discrepancy

Complex data are often represented as a graph, which in turn can often be viewed as a realisation of a random graph, such as an inhomogeneous random graph model (IRG). For general fast goodness-of-fit tests in high dimensions, kernelised Stein discrepancy (KSD) tests are a powerful tool. Here, we develop a KSD-type test for IRG models that can be carried out with a single observation of the network. The test applies to networks of any size, but is particularly relevant for small networks for which asymptotic tests are not warranted. We also provide theoretical guarantees.