A measure of centrality based on the spectrum of the Laplacian

Details A measure of centrality based on the spectrum of the Laplacian A measure of centrality based on the spectrum of the Laplacian

2011-12-20

arxiv.org/abs/1112.4758v1

Physics

Data Analysis, Statistics and Probability

12 pages, 6 figures, 2 tables

Scientific paper

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.

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