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ON THE NONNEGATIVITY OF THE DIRICHLET ENERGY OF A WEIGHTED GRAPH

Part of: Basic linear algebra Special matrices

Published online by Cambridge University Press:  17 December 2021

KYLE BRODER Open the ORCID record for KYLE BRODER [Opens in a new window]
KYLE BRODER*
Affiliation:
Mathematical Sciences Institute, Australian National University, Acton, ACT 2601, Australia and BICMR, Peking University, Beijing 100871, PR China
*
e-mail: kyle.broder@anu.edu.au
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Abstract

Motivated by considerations of the quadratic orthogonal bisectional curvature, we address the question of when a weighted graph (with possibly negative weights) has nonnegative Dirichlet energy.

Keywords

Dirichlet energyweighted graphEuclidean distance matrixcones of matricescurvature

MSC classification

Primary: 15B48: Positive matrices and their generalizations; cones of matrices
Secondary: 15A18: Eigenvalues, singular values, and eigenvectors
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 106 , Issue 2 , October 2022 , pp. 301 - 305
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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