Every nonsingular spherical Euclidean distance matrix is a resistance distance matrix

Name: Every nonsingular spherical Euclidean distance matrix is a resistance distance matrix
Creator: Ernesto Estrada
Keywords: Distance in graphs, Graphs and linear algebra (matrices, eigenvalues, etc.), Euclidean distance matrix, algebraic graph theory, Discrete geometry, Euclidean distance matrix (EDM), communicability distance, Spectral graph theory, spectral graph theory, Resistance distance

Ernesto Estrada

Found an issue? Give us feedback

downloadFull-Text

Recolector de Cienci...arrow_drop_down

Recolector de Ciencia Abierta, RECOLECTA

Article . 2024 . Peer-reviewed

Full-Text: https://doi.org/10.1016/j.laa.2022.09.025

Data sources: Recolector de Ciencia Abierta, RECOLECTA

Linear Algebra and its Applications

Article . 2023 . Peer-reviewed

License: CC BY

Data sources: Crossref

DIGITAL.CSIC

Article . 2024 . Peer-reviewed

Data sources: DIGITAL.CSIC

zbMATH Open

Article . 2023

Data sources: zbMATH Open

Every nonsingular spherical Euclidean distance matrix is a resistance distance matrix

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

Copyright policy )

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

- Summary
- Subjects
- Metrics

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.

Peer reviewed

Country

Spain

Related Organizations

Keywords

Distance in graphs, Graphs and linear algebra (matrices, eigenvalues, etc.), Euclidean distance matrix, algebraic graph theory, Discrete geometry, Euclidean distance matrix (EDM), communicability distance, Spectral graph theory, spectral graph theory, Resistance distance, Positive matrices and their generalizations; cones of matrices, resistance distance, spherical EDM, Spherical EDM, Communicability distance, Algebraic graph theory

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	9
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 10%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Top 10%