Name: Every nonsingular spherical Euclidean distance matrix is a resistance distance matrix
Creator: Ernesto Estrada
Keywords: Euclidean distance matrix (EDM), Spectral graph theory, Spherical EDM, Communicability distance, Resistance distance, 0101 mathematics, 01 natural sciences, Algebraic graph theory

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2023 English Publisher:Elsevier BVJournal:Linear Algebra and its Applications, volume 656, pages 198-209 (issn: 0024-3795,

Authors: Ernesto Estrada;

doi: 10.1016/j.laa.2022.09.025

handle: 10261/351427

Every nonsingular spherical Euclidean distance matrix is a resistance distance matrix

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Abstract

The communicability distance (Estrada (2012) [5]) is a useful metric to characterize alternative navigational routes in graphs. Here we prove that it is the resistance distance between a pair of nodes in a weighted graph. We extend this result and prove that every nonsingular Euclidean distance matrix is the resistance distance matrix of a weighted graph. We briefly analyze some mathematical properties of the communicability Laplacian matrix which emerges from the current analysis.

The author thanks anonymous referee for important corrections on the original version. Financial support by the grant PID2019-107603GB-I00 of the MCIN/AEI/0.13039/501100011033/ is also acknowledged.

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Keywords

Euclidean distance matrix (EDM), Spectral graph theory, Spherical EDM, Communicability distance, Resistance distance, Algebraic graph theory

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