The Gromov-Wasserstein distance between networks and stable network invariants

TL;DR

This paper introduces a new metric for weighted, directed networks called the network Gromov-Wasserstein distance, along with invariants based on optimal transport, and demonstrates their effectiveness through simulations and real-world data.

Contribution

It defines a novel network distance metric and associated invariants, providing theoretical insights and practical tools for network comparison.

Findings

The network Gromov-Wasserstein distance is sensitive to outliers.

Network invariants approximate the distance using lower bounds.

The methods perform well on simulated and real-world network data.

Abstract

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. This may be of independent interest for benchmarking purposes.