Abstract: One of the main applications of the “spectral networks” of Gaiotto-Moore-Neitzke is the abelianization map, which provides nice coordinate systems on various moduli spaces of flat connections on a Riemann surface C. But many mathematical properties of spectral networks remain to be established in generality - in particular the question of the uniqueness of this abelianization process is open. I will describe a particular instance of this question and its solution as it arises in the study of some networks for moduli spaces which are (roughly) Grassmannians, and discuss the relation between the spectral coordinates and the well-known cluster structure on these varieties.