  We express the discrete Ricci curvature of a graph as the minimal eigenvalue
of a family of matrices, one for each vertex of a graph whose entries depend on
the local adjaciency structure of the graph. Using this method we compute or
bound the Ricci curvature of Cayley graphs of finite Coxeter groups and affine
Weyl groups. As an application we obtain an isoperimetric inequality that holds
for all Cayley graphs of finite Coxeter groups.
