Spectral embedding of weighted graphs
This work addresses the challenge of analyzing weighted networks like count or p-value graphs for researchers in network science, offering incremental improvements to existing methods.
The paper tackles the problem of improving spectral embedding for weighted graphs by exploring edge-weight transformations, showing that tempering or thresholding can significantly enhance community distinguishability in theory and practice.
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.