  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.
