Valid Bootstraps for Networks with Applications to Network Visualisation

Quantifying uncertainty in networks is an important step in modelling relationships and interactions between entities. We consider the challenge of bootstrapping an inhomogeneous random graph when only a single observation of the network is made and the underlying data generating function is unknown. We utilise an exchangeable network test that can empirically validate bootstrap samples generated by any method, by testing if the observed and bootstrapped networks are statistically distinguishable. We find that existing methods fail this test. To address this, we propose a principled, novel, distribution-free network bootstrap using k-nearest neighbour smoothing, that can regularly pass this exchangeable network test in both synthetic and real-data scenarios. We demonstrate the utility of this work in combination with the popular data visualisation method t-SNE, where uncertainty estimates from bootstrapping are used to explain whether visible structures represent real statistically sound structures.