Adapts the Debye volume-to-interface ratio to graphs as twice the total edges divided by sign-change edges to assign effective length scales to Laplacian eigenvectors, producing dispersion relations and densities of states on networks including C. elegans, power grids, and tree graphs with shortcuts
Further basic properties of the normalized spectrum for a graphGwith Nvertices are listed in Lemma 1.7 of Ref
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Effective length scales, dispersion relations, and discrete densities of states for Laplacian eigenvectors on complex networks
Adapts the Debye volume-to-interface ratio to graphs as twice the total edges divided by sign-change edges to assign effective length scales to Laplacian eigenvectors, producing dispersion relations and densities of states on networks including C. elegans, power grids, and tree graphs with shortcuts