  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 t-SNE, a widely used method for nonlinear dimensionality
reduction and data visualization. We also introduce t-SNE-$\Pi$, a
high-performance software for 2D, 3D embedding of large sparse graphs on
personal computers with superior efficiency. It empowers SG-t-SNE with modern
computing techniques for exploiting in tandem both matrix structures and memory
architectures. We present elucidating embedding results on one synthetic graph
and four real-world networks.
