Our　goal　is　to　efficiently　compute　low-dimensional　latent　coordinates　for　nodes　in　an　input　graph-known　as　graph　embedding-for　subsequent　data　processing　such　as　clustering.　Focusing　on　finite　graphs　that　are　interpreted　as　uniform　samples　on　continuous　manifolds　(called　manifold　graphs),　we　leverage　existing　fast　extreme　eigenvector　computation　algorithms　for　speedy　execution.　We　first　pose　a　generalized　eigenvalue　problem　for　sparse　matrix　pair　(A;B),　where　A　=　L　mu　Q　+　epsilon　I　is　a　sum　of　graph　Laplacian　L　and　disconnected　two-hop　difference　matrix　Q.　Eigenvector　v　minimizing　Rayleigh　quotient　v(inverted　perpendicular)Av/v(inverted　perpendicular)v　thus　minimizes　1-hop　neighbor　distances　while　maximizing　distances　between　disconnected　2-hop　neighbors,　preserving　graph　structure.　Matrix　B　=　diag(fbig)　that　defines　eigenvector　orthogonality　is　then　chosen　so　that　boundary　/　interior　nodes　in　the　sampling　domain　have　the　same　generalized　degrees.　K　-dimensional　latent　vectors　for　the　N　graph　nodes　are　the　first　K　generalized　eigenvectors　for　(A　,　B),　computed　in　O(N)　using　LOBPCG,　where　K　＜＜　N.　Experiments　show　that　our　embedding　is　among　the　fastest　in　the　literature,　while　producing　the　best　clustering　performance　for　manifold　graphs.