A large family of shape comparison methods is based on a medial axis transform combined with an encoding of the skeleton by a graph. Despite many qualities this encoding of shapes suffers from the non continuity of the medial axis transform. In this paper, we propose to integrate robustness against structural noise inside a graph kernel. This robustness is based on a selection of the paths according to their relevance and on path editions. This kernel is positive semi-definite and several experiments prove the efficiency of our approach compared to alternative kernels. Key words: Shape, Skeleton, Support Vector Machine, Graph Kernel