A graph discretization of vector Laplacian
Résumé
As known, the scalar Laplacian gives the celebrated Laplacian matrix of a graph. In this paper, we determine the graph matrix presentation of vector Laplacian (or Helmholtz operator), named as Helmholtzian matrix. To compare the difference and similarity with previous graph matrices, we study the limit points of spectral radius and characterize the connected graphs with spectral radius at most 4.38+ via Helmholtzian matrix. Finally, we discuss the potential applications of Helmholtzian spectra of graphs in the simplicial networks and small-world networks.