Document Type


Publication Date


Publication Title

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics


Department of Mathematics


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 net- works 1-spectral centrality behaves similarly to other standard centralities, for dense weighted net- works 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.



Original Citation

Pauls SD, Remondini D. Measures of centrality based on the spectrum of the Laplacian. Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 2):066127. doi: 10.1103/PhysRevE.85.066127. Epub 2012 Jun 20. PMID: 23005182.