Graph learning from band-limited data by graph Fourier transform analysis

•We reveal the intrinsic relation between the unknown frequency-domain representation of general band-limited graph signals and the graph Fourier transform basis.•A new analytical expression is derived to determine the graph Fourier transform basis of observed band-limited signals.•Given the graph Fourier transform basis and the statistical knowledge of the graph Laplacian, the estimation of the eigenvalues of the graph Laplacian is convex and efficiently solved using the alternating direction method of multipliers.