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