The Gromov-Wasserstein distance between networks and stable network invariants

Understand

We define a metric---the network Gromov-Wasserstein distance---on weighted, directed networks that is sensitive to the presence of outliers.

• In addition to proving its theoretical properties, we supply network invariants based on optimal transport that approximate this distance by means of lower bounds.
• We test these methods on a range of simulated network datasets and on a dataset of real-world global bilateral migration.
• For our simulations, we define a network generative model based on the stochastic block model.