A measure of centrality based on the spectrum of the Laplacian

TL;DR

This paper introduces k-spectral centralities, a new family of importance measures based on the graph Laplacian spectrum, offering unique insights especially in dense weighted networks.

Contribution

The paper presents a novel family of centrality measures derived from the Laplacian spectrum, expanding the tools for network analysis with spectrally interpreted importance metrics.

Findings

k-Spectral centralities behave similarly to standard measures in sparse unweighted networks

In dense weighted networks, they exhibit distinct properties from traditional centralities

They provide a new perspective on node and subnetwork relevance in various network types

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.