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arXiv · 2606.24261

A combinatorial Approach to $\alpha$-Ricci and Lin-Lu-Yau Ricci curvatures on Graphs

Jaewoo Jung·Young Soo Kwon·Seungjae Lee·Jihye Park
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Abstract

In this paper, we study the $\alpha$-Ricci curvature and the Lin-Lu-Yau Ricci curvature on simple, connected, and locally finite graphs. For regular graphs, we introduce a combinatorial construction of optimal transport plans realizing the 1-Wasserstein distance and use it to derive exact formulas for the $\alpha$-Ricci curvature and the Lin-Lu-Yau Ricci curvature. This yields a combinatorial proof of the known curvature formulas. Furthermore, for non-regular graphs, we characterize conditions on the size of common neighborhoods that guarantee either non-negative or vanishing Lin-Lu-Yau Ricci curvature.

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Jaewoo Jung, Young Soo Kwon, Seungjae Lee, Jihye Park. 2026-06-23. A combinatorial Approach to $\alpha$-Ricci and Lin-Lu-Yau Ricci curvatures on Graphs. https://arxiv.org/abs/2606.24261

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