  In this paper we propose a lightning fast graph embedding method called
one-hot graph encoder embedding. It has a linear computational complexity and
the capacity to process billions of edges within minutes on standard PC --
making it an ideal candidate for huge graph processing. It is applicable to
either adjacency matrix or graph Laplacian, and can be viewed as a
transformation of the spectral embedding. Under random graph models, the graph
encoder embedding is approximately normally distributed per vertex, and
asymptotically converges to its mean. We showcase three applications: vertex
classification, vertex clustering, and graph bootstrap. In every case, the
graph encoder embedding exhibits unrivalled computational advantages.
