Using Gromov-Wasserstein distance to explore sets of networks

Abstract

In many fields such as social sciences or biology, relations between data or variables are presented as networks. To compare these networks, a meaningful notion of distance between networks is highly desired. The aim of this Master thesis is to study, implement, and apply one Gromov-Wasserstein type of distance introduced by F.Memoli (2011) in his paper "Gromov-Wasserstein Distances and the Metric Approach to Object Matching" to study sets of complex networks. Taking into account theoretical underpinnings introduced in this paper we represent some real world networks as metric measure spaces and compare them on basis of Gromov-Wasserstein distance.