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We develop a method based on spectral graph theory to approximate the eigenvalues and eigenfunctions of the Laplace-Beltrami operator of a compact riemannian manifold. The method is applied to a closed hyperbolic surface of genus two. The results obtained agree with the ones obtained by other authors by different methods, and they serve as experimental evidence supporting the conjectured fact that the generic eigenfunctions belonging to the first nonzero eigenvalue of a closed hyperbolicdoi:10.1016/j.difgeo.2017.03.002 fatcat:5yppkp5yuvewxasx3xmukbrqva