The Topological "Shape" of Brexit

TL;DR

This paper applies persistent homology, a topological data analysis method, to Brexit-related datasets to demonstrate how algebraic topology can reveal the shape of complex political data.

Contribution

It illustrates the use of weight rank clique and Vietoris--Rips filtrations in analyzing Brexit data, highlighting their strengths and weaknesses.

Findings

Demonstrates the application of persistent homology to political data

Shows the effectiveness of topological methods in revealing data structure

Provides insights into the shape of Brexit-related datasets

Abstract

Persistent homology is a method from computational algebraic topology that can be used to study the "shape" of data. We illustrate two filtrations --- the weight rank clique filtration and the Vietoris--Rips (VR) filtration --- that are commonly used in persistent homology, and we apply these filtrations to a pair of data sets that are both related to the 2016 European Union "Brexit" referendum in the United Kingdom. These examples consider a topical situation and give useful illustrations of the strengths and weaknesses of these methods.