Eulerian tour algorithms for data visualization and the PairViz package. 𝙿𝚊𝚒𝚛𝚅𝚒𝚣 is an R package that produces orderings of statistical objects for visualization purposes. We abstract the ordering problem to one of constructing edge-traversals of (possibly weighted) graphs. 𝙿𝚊𝚒𝚛𝚅𝚒𝚣 implements various edge traversal algorithms which are based on Eulerian tours and Hamiltonian decompositions. We describe these algorithms, their 𝙿𝚊𝚒𝚛𝚅𝚒𝚣 implementation and discuss their properties and performance. We illustrate their application to two visualization problems, that of assessing rater agreement, and model comparison in regression.