We introduce a nonlinear method for directly embedding large, sparse, stochastic graphs into low-dimensional spaces, without requiring vertex features to reside in or be transformed into, a metric space. Graph data and models are prevalent in real-world applications. Direct graph embedding is fundamental to many graph analysis tasks, in addition to graph visualization. We name the novel approach SG-t-SNE, as it is inspired by and builds upon the core principle of, a widely used method for nonlinear dimensionality reduction and data visualization. We also introduce t-SNE-Π, a high-performance software for 2D, 3D embedding of large sparse graphs on personal computers with superior efficiency. It empowers with modern computing techniques for exploiting in tandem both matrix structures and memory architectures. We present elucidating embedding results on two synthetic graphs and six real-world networks (one synthetic and four real-world networks are shown in the article).