Abstract
We present non-iterative methods for graph embedding in flat and curved manifold and acriterion to assess the quality of the embedding for the purpose of determining what is the optimal latent geometry of a graph. To date, graph embedding procedures have been used in data dimension reduction problems for the purpose of simpler and more efficient data analysis, but little has been done to use them as a tool for the estimation of the latent geometry. The latent geometry of a graph is important since it explains graph organizational structure and dynamics. Advancing the state of the art in this direction is of particular importance for the study of biological networks, since these networks exhibit a high degree of organizational complexity that is difficult to identify with standard analyses of node centrality measures.