The Topological "Shape" of Brexit

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.

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