In the presented experimental study, we compare the classification power of two variations of the same graph kernel. One variation is designed to produce semi-definite positive kernel matrices (K matching) and is an approximation of the other one, which is indefinite (Kmax). We show that using adaptated tools to deal with indefiniteness (KSVM), the original indefinite kernel outperforms its positive definite approximate version. We also propose a slight improvement of the KSVM method, which produces non sparse solutions, by adding a fast post-processing step that gives a sparser solution.