Measures of centrality based on the spectrum of the Laplacian

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 spec...

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Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2012-06, Vol.85 (6 Pt 2), p.066127-066127, Article 066127
Main Authors: Pauls, Scott D, Remondini, Daniel
Format: Article
Language:English
Subjects:
Algorithms
Computer Simulation
Models, Biological
Models, Theoretical
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Summary: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.
ISSN:1539-3755
1550-2376
DOI:10.1103/PhysRevE.85.066127