On Steinerberger curvature and graph distance matrices
Journal
Discrete Mathematics
Journal Volume
348
Journal Issue
8
Start Page
114475
ISSN
0012-365X
Date Issued
2025-08
Author(s)
Wei-Chia Chen
Abstract
Steinerberger proposed a notion of curvature on graphs involving the graph distance matrix (J. Graph Theory, 2023). We show that nonnegative curvature is almost preserved under three graph operations. We characterize the distance matrix and its null space after adding an edge between two graphs. Let D be the graph distance matrix and 1 be the all-one vector. We provide a way to construct graphs so that the linear system Dx=1 does not have a solution.
Publisher
Elsevier BV
Type
journal article