  When analyzing weighted networks using spectral embedding, a judicious
transformation of the edge weights may produce better results. To formalize
this idea, we consider the asymptotic behavior of spectral embedding for
different edge-weight representations, under a generic low rank model. We
measure the quality of different embeddings -- which can be on entirely
different scales -- by how easy it is to distinguish communities, in an
information-theoretic sense. For common types of weighted graphs, such as count
networks or p-value networks, we find that transformations such as tempering or
thresholding can be highly beneficial, both in theory and in practice.
