I am a PhD. in pure mathematics.
- Could you please illustrate the following statement: the eigenvectors of a graph Laplacian behave similarly to a Fourier basis, motivating the development of graph-based Fourier analysis theory.
- I am reading the interesting paper, but could not get how the Fourier transform is extended to the graph Fourier transform as illustrated on page 23. Indeed, why should the matrix V be considered as the extension of (discrete) Fourier transform?