On Steinerberger curvature and graph distance matrices

被引：0

作者：

Chen, Wei-Chia ^{[1
,3
]}

Tsui, Mao-Pei ^{[1
,2
]}

机构：

[1] Natl Ctr Theoret Sci, Math Div, Taipei 106, Taiwan

[2] Natl Taiwan Univ, Dept Math, Taipei 106, Taiwan

[3] Iowa State Univ, Dept Math, Ames, IA 50011 USA

来源：

DISCRETE MATHEMATICS | 2025年 / 348卷 / 08期

关键词：

Graph curvature; Distance matrix; Perron-Frobenius; RICCI CURVATURE;

D O I：

10.1016/j.disc.2025.114475

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页数：12

共 16 条

[1]

Bapat Ravindra B., 2014, Graphs and Matrices, Vsecond, P115

[2] Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature [J].

Cushing, D. ;

Kamtue, S. ;

Koolen, J. ;

Liu, S. ;

Muench, F. ;

Peyerimhoff, N. .

ADVANCES IN MATHEMATICS, 2020, 369

[3] The Graph Curvature Calculator and the Curvatures of Cubic Graphs [J].

Cushing, David ;

Kangaslampi, Riikka ;

Lipiainen, Valtteri ;

Liu, Shiping ;

Stagg, George W. .

EXPERIMENTAL MATHEMATICS, 2022, 31 (02) :583-595

[4]

Denny Natalie, 2020, Master's project

[5] Graph curvature via resistance distance [J].

Devriendt, Karel ;

Ottolini, Andrea ;

Steinerberger, Stefan .

DISCRETE APPLIED MATHEMATICS, 2024, 348 :68-78

[6] Discrete curvature on graphs from the effective resistance* [J].

Devriendt, Karel ;

Lambiotte, Renaud .

JOURNAL OF PHYSICS-COMPLEXITY, 2022, 3 (02)

[7]

Dudarov William, 2023, arXiv

[8]

Hammack Richard, 2011, Discrete Mathematics and Its Applications, Vsecond, P49

[9]

HORN R. A., 2013, Matrix Analysis, VSecond

[10] RICCI CURVATURE OF GRAPHS [J].

Lin, Yong ;

Lu, Linyuan ;

Yau, Shing-Tung .

TOHOKU MATHEMATICAL JOURNAL, 2011, 63 (04) :605-627

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