title: Measures of centrality based on the spectrum of the Laplacian.
abstract: We introduce a family of new centralities, the k-spectral centralities. k-spectral centrality is a measurement of importance with respect to the deformation of the graph Laplacian associated with the graph. Due to this connection, k-spectral centralities have various interpretations in terms of spectrally determined information. We explore this centrality in the context of several examples. While for sparse unweighted networks 1-spectral centrality behaves similarly to other standard centralities, for dense weighted networks they show different properties. In summary, the k-spectral centralities provide a novel and useful measurement of relevance (for single network elements as well as whole subnetworks) distinct from other known measures.
authors.affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755, USA. scott.d.pauls@dartmouth.edu
authors.forename: Scott D
authors.initials: SD
authors.lastname: Pauls
authors.forename: Daniel
authors.initials: D
authors.lastname: Remondini
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008954:Models, Biological; D008962:Models, Theoretical