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

2017/12/10 by Taiki Yamada, Yamada, Taiki
Mathematics · #35J05 #Differential Geometry (math.DG) #FOS: Mathematics #Primary 05C12 #Secondary 52C99 #Spectral Theory (math.SP) #math.DG #math.SP #msc:05C12 #msc:35J05 #msc:52C99

paper · pdf · doi:10.48550/arxiv.1712.03465

14pages, 5 figures

arxiv created 2017/12/10 · arxiv updated 2017/12/12

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.

Related

• Ricci curvature and eigenvalue estimate on locally finite graphs
• The Ricci curvature on simplicial complexes
• Integral Ricci Curvature for Graphs
• Coarse Ricci curvature of hypergraphs and its generalization
• Spectrally positive Bakry-Émery Ricci curvature on graphs