where "B"("x","r") denotes the ball of radius "r" around the point "x" in the Riemannian distance or in the graph distance. In general, the opposite is not true, i.e. even uniformly exponential volume growth does not imply any kind of isoperimetric inequality. A simple example can be had by taking the graph Z (i.e. all the integers with edges between "n" and "n" + 1) and connecting to the vertex "n" a complete binary tree of height |"n"|. Both properties (exponential growth and 0 isoperimetric dimension) are easy to verify.