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Graph and Hodge Laplacians: Similarity and Difference
[article]
2022
arXiv
pre-print
As key subjects in spectral geometry and spectral graph theory respectively, the Hodge Laplacian and the graph Laplacian share similarities in their realization of vector calculus, through the gradient, curl, and divergence, and by revealing the topological dimension and geometric shape of data. These similarities are reflected in the popular usage of "Hodge Laplacians on graphs" in the literature. However, these Laplacians are intrinsically different in their domains of definitions and
arXiv:2204.12218v1
fatcat:dlc3azyyjzgeled2wxqjno3wbu