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arXiv · 2409.15667

Ricci Curvature Formula: Applications to Bonnet-Myers Sharp Irregular Graphs

Yupei Li·Linyuan Lu
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Abstract

In this paper, we establish a simple formula for computing the Lin-Lu-Yau Ricci curvature on graphs. For any edge $xy$ in a simple locally finite graph $G$, the curvature $κ(x,y)$ can be expressed as a cost function of an optimal bijection between two blow-up sets of the neighbors of $x$ and $y$. Utilizing this approach, we derive several results including a structural theorem for the Bonnet-Myers sharp irregular graphs of diameter $3$ and a theorem on $C_3$-free Bonnet-Myers sharp graphs.

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Yupei Li, Linyuan Lu. 2024-11-22. Ricci Curvature Formula: Applications to Bonnet-Myers Sharp Irregular Graphs. https://arxiv.org/abs/2409.15667

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