A Pure Hypothesis Test for Inhomogeneous Random Graph Models Based on a Kernelised Stein Discrepancy

TL;DR

This paper introduces a kernelised Stein discrepancy-based goodness-of-fit test for inhomogeneous random graph models that can be applied to single network observations, especially useful for small networks.

Contribution

It develops a novel KSD-type test for IRG models that works with a single network sample and provides theoretical guarantees.

Findings

Test applicable to networks of any size, including small networks.

Provides theoretical guarantees for the test's validity.

Effective for high-dimensional network data.

Abstract

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.