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 a network of any size, but is particularly interesting for small networks for which asymptotic tests are not warranted. We also provide theoretical guarantees.

翻译：复杂数据常以图的形式表示，而图本身通常可视为随机图的一次实现，例如非均匀随机图模型（IRG）。针对高维场景下的通用快速拟合优度检验，核化Stein差异（KSD）检验是一种强有力的工具。本文针对IRG模型开发了一种KSD型检验方法，该方法仅需单次网络观测即可实施。该检验适用于任意规模的网络，但对于渐进检验不适用的小规模网络尤其具有研究价值。文中同时提供了相应的理论保证。