  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.
