An estimate of the first non-zero eigenvalue of the Laplacian by the Ricci curvature on edges of graphs

Taiki Yamada

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arXiv · 1712.03465

An estimate of the first non-zero eigenvalue of the Laplacian by the Ricci curvature on edges of graphs

Taiki Yamada

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Abstract

We define the distance between edges of graphs and study the coarse Ricci curvature on edges. We consider the Laplacian on edges based on the Jost-Horak's definition of the Laplacian on simplicial complexes. As one of our main results, we obtain an estimate of the first non-zero eigenvalue of the Laplacian by the Ricci curvature for a regular graph.

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Taiki Yamada. 2017-12-10. An estimate of the first non-zero eigenvalue of the Laplacian by the Ricci curvature on edges of graphs. https://arxiv.org/abs/1712.03465

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