Proving a Kernel

Got this from the paper "Graph Kernels for Chemical Classification", by Ralaivola et. al, published in Neural Networks 2005.

It looks like, to prove a kernel, you need to show that the function is symmetric (ie, k(u,v) = k(v,u) ), that it's continuous, and that it is "a positive definite kernel" (ie, that the square n x n matrix K = (k(u_i, u_j))_{1 <= i, j <= n} is positive semi-definite...ie, all its eigenvalues are non-negative).

This would make it a Mercer Kernel.