Probabilistic graphical models encode the conditional independence properties satisfied by a joint probability distribution. If the distribution is Gaussian, the edges of an undirected graphical model correspond to non-zero entries of the precision matrix. Generalizing this result to continuous non-Gaussian distributions, one can show that an edge exists if and only if an entry of the Hessian of the log density is non-zero (everywhere). But evaluation of the log density requires density estimation: for this, we propose the graph-learning algorithm SING (Sparsity Identification in Non-Gaussian distributions), which uses triangular transport for the density estimation step; this choice is advantageous as triangular maps inherit sparsity from conditional independence in the target distribution. Loosely speaking, the more non-Gaussian the distribution, the more difficult the transport problem. For a broad class of non-Gaussian distributions, however, estimating the Hessian of the log density is much easier than estimating the density itself. For the transport community, this result serves as a sort of goal-oriented transport framework, in which the particular goal of graph learning greatly simplifies the transport problem.